LMFDB - Embedded newform 462.2.bc.b.95.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.6
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(-0.840980 - 1.51418i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.12093 - 2.51765i) q^{5} +(1.59380 - 0.678098i) q^{6} +(2.40939 - 1.09308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.58551 + 2.54680i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.840980 - 1.51418i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.12093 - 2.51765i) q^{5} +(1.59380 - 0.678098i) q^{6} +(2.40939 - 1.09308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.58551 + 2.54680i) q^{9} +(2.38669 + 1.37795i) q^{10} +(-3.22424 + 0.777358i) q^{11} +(0.507786 + 1.65594i) q^{12} +(0.533779 - 0.734683i) q^{13} +(0.835242 + 2.51045i) q^{14} +(-4.75486 + 0.419999i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.233441 - 2.22105i) q^{17} +(-2.36711 - 1.84303i) q^{18} +(-1.38320 - 6.50747i) q^{19} +(-1.61988 + 2.22958i) q^{20} +(-3.68138 - 2.72901i) q^{21} +(-0.436075 - 3.28783i) q^{22} +(-4.85329 + 2.80205i) q^{23} +(-1.69995 + 0.331911i) q^{24} +(-1.73642 - 1.92849i) q^{25} +(0.674863 + 0.607650i) q^{26} +(5.18970 + 0.258941i) q^{27} +(-2.58401 + 0.568253i) q^{28} +(-1.35518 - 4.17081i) q^{29} +(0.0793202 - 4.77271i) q^{30} +(-0.217640 + 0.0968995i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.88858 + 4.22835i) q^{33} +2.23328 q^{34} +(-0.0512330 - 7.29127i) q^{35} +(2.08037 - 2.16150i) q^{36} +(7.25637 - 8.05901i) q^{37} +(6.61640 - 0.695412i) q^{38} +(-1.56134 - 0.190385i) q^{39} +(-2.04804 - 1.84406i) q^{40} +(-1.32308 + 4.07202i) q^{41} +(3.09886 - 3.37595i) q^{42} +8.42414i q^{43} +(3.31540 - 0.0900140i) q^{44} +(4.63470 + 6.84652i) q^{45} +(-2.27939 - 5.11959i) q^{46} +(-2.18126 - 10.2620i) q^{47} +(-0.152399 - 1.72533i) q^{48} +(4.61035 - 5.26732i) q^{49} +(2.09943 - 1.52532i) q^{50} +(-3.16675 + 2.22133i) q^{51} +(-0.674863 + 0.607650i) q^{52} +(1.15816 + 2.60126i) q^{53} +(-0.799994 + 5.13420i) q^{54} +(-1.65703 + 8.98886i) q^{55} +(-0.295038 - 2.62925i) q^{56} +(-8.69025 + 7.56707i) q^{57} +(4.28962 - 0.911786i) q^{58} +(-1.31314 + 6.17786i) q^{59} +(4.73828 + 0.577770i) q^{60} +(1.19589 - 2.68601i) q^{61} +(-0.0736192 - 0.226576i) q^{62} +(-1.03625 + 7.86932i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.25135 - 2.16739i) q^{65} +(-4.61165 + 3.42530i) q^{66} +(2.80878 - 4.86495i) q^{67} +(-0.233441 + 2.22105i) q^{68} +(8.32433 + 4.99230i) q^{69} +(7.25668 + 0.711193i) q^{70} +(-2.57763 - 3.54780i) q^{71} +(1.93220 + 2.29491i) q^{72} +(-2.21647 + 10.4277i) q^{73} +(7.25637 + 8.05901i) q^{74} +(-1.45979 + 4.25107i) q^{75} +6.65285i q^{76} +(-6.91874 + 5.39731i) q^{77} +(0.352547 - 1.53289i) q^{78} +(4.75825 + 0.500112i) q^{79} +(2.04804 - 1.84406i) q^{80} +(-3.97235 - 8.07592i) q^{81} +(-3.91141 - 1.74147i) q^{82} +(3.07387 - 2.23330i) q^{83} +(3.03354 + 3.43477i) q^{84} +(-5.85348 - 1.90191i) q^{85} +(-8.37800 - 0.880563i) q^{86} +(-5.17569 + 5.55956i) q^{87} +(-0.257033 + 3.30665i) q^{88} +(-3.00107 + 1.73267i) q^{89} +(-7.29347 + 3.89365i) q^{90} +(0.483015 - 2.35360i) q^{91} +(5.32981 - 1.73176i) q^{92} +(0.329755 + 0.248056i) q^{93} +(10.4338 - 1.09664i) q^{94} +(-17.9340 - 3.81199i) q^{95} +(1.73181 + 0.0287819i) q^{96} +(14.4550 + 10.5022i) q^{97} +(4.75655 + 5.13568i) q^{98} +(3.13227 - 9.44399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.840980	−	1.51418i	−0.485540	−	0.874214i
$3$	−0.840980	−	1.51418i	−0.485540	−	0.874214i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	1.12093	−	2.51765i	0.501295	−	1.12593i	−0.468823	−	0.883292i	$-0.655322\pi$
$5$	1.12093	−	2.51765i	0.501295	−	1.12593i	0.970118	−	0.242634i	$-0.0780115\pi$
$6$	1.59380	−	0.678098i	0.650664	−	0.276832i
$7$	2.40939	−	1.09308i	0.910665	−	0.413146i
$7$	2.40939	−	1.09308i	0.910665	−	0.413146i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.58551	+	2.54680i	−0.528502	+	0.848932i
$10$	2.38669	+	1.37795i	0.754737	+	0.435747i
$11$	−3.22424	+	0.777358i	−0.972145	+	0.234382i
$11$	−3.22424	+	0.777358i	−0.972145	+	0.234382i
$12$	0.507786	+	1.65594i	0.146585	+	0.478030i
$13$	0.533779	−	0.734683i	0.148044	−	0.203764i	−0.728554	−	0.684988i	$-0.759807\pi$
$13$	0.533779	−	0.734683i	0.148044	−	0.203764i	0.876598	+	0.481224i	$0.159807\pi$
$14$	0.835242	+	2.51045i	0.223228	+	0.670947i
$15$	−4.75486	+	0.419999i	−1.22770	+	0.108443i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.233441	−	2.22105i	−0.0566178	−	0.538683i	−0.985664	−	0.168719i	$-0.946037\pi$
$17$	−0.233441	−	2.22105i	−0.0566178	−	0.538683i	0.929046	−	0.369963i	$-0.120630\pi$
$18$	−2.36711	−	1.84303i	−0.557934	−	0.434407i
$19$	−1.38320	−	6.50747i	−0.317329	−	1.49291i	−0.790783	−	0.612097i	$-0.790326\pi$
$19$	−1.38320	−	6.50747i	−0.317329	−	1.49291i	0.473454	−	0.880818i	$-0.343007\pi$
$20$	−1.61988	+	2.22958i	−0.362217	+	0.498549i
$21$	−3.68138	−	2.72901i	−0.803342	−	0.595518i
$22$	−0.436075	−	3.28783i	−0.0929715	−	0.700968i
$23$	−4.85329	+	2.80205i	−1.01198	+	0.584267i	−0.911771	−	0.410699i	$-0.865285\pi$
$23$	−4.85329	+	2.80205i	−1.01198	+	0.584267i	−0.100209	+	0.994966i	$0.531951\pi$
$24$	−1.69995	+	0.331911i	−0.347001	+	0.0677510i
$25$	−1.73642	−	1.92849i	−0.347283	−	0.385697i
$26$	0.674863	+	0.607650i	0.132352	+	0.119170i
$27$	5.18970	+	0.258941i	0.998758	+	0.0498333i
$28$	−2.58401	+	0.568253i	−0.488331	+	0.107390i
$29$	−1.35518	−	4.17081i	−0.251650	−	0.774500i	−0.994471	−	0.105010i	$-0.966513\pi$
$29$	−1.35518	−	4.17081i	−0.251650	−	0.774500i	0.742821	−	0.669490i	$-0.233487\pi$
$30$	0.0793202	−	4.77271i	0.0144818	−	0.871375i
$31$	−0.217640	+	0.0968995i	−0.0390893	+	0.0174037i	−0.426188	−	0.904635i	$-0.640144\pi$
$31$	−0.217640	+	0.0968995i	−0.0390893	+	0.0174037i	0.387099	+	0.922038i	$0.373477\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.88858	+	4.22835i	0.676915	+	0.736061i
$34$	2.23328			0.383004
$35$	−0.0512330	−	7.29127i	−0.00865996	−	1.23245i
$36$	2.08037	−	2.16150i	0.346728	−	0.360250i
$37$	7.25637	−	8.05901i	1.19294	−	1.32489i	0.259678	−	0.965695i	$-0.416383\pi$
$37$	7.25637	−	8.05901i	1.19294	−	1.32489i	0.933261	−	0.359199i	$-0.116950\pi$
$38$	6.61640	−	0.695412i	1.07332	−	0.112811i
$39$	−1.56134	−	0.190385i	−0.250015	−	0.0304860i
$40$	−2.04804	−	1.84406i	−0.323823	−	0.291572i
$41$	−1.32308	+	4.07202i	−0.206630	+	0.635942i	0.793012	+	0.609205i	$0.208512\pi$
$41$	−1.32308	+	4.07202i	−0.206630	+	0.635942i	−0.999643	+	0.0267365i	$0.991488\pi$
$42$	3.09886	−	3.37595i	0.478165	−	0.520920i
$43$			8.42414i			1.28467i	0.766424	+	0.642335i	$0.222034\pi$
$43$			8.42414i			1.28467i	−0.766424	+	0.642335i	$0.777966\pi$
$44$	3.31540	−	0.0900140i	0.499816	−	0.0135701i
$45$	4.63470	+	6.84652i	0.690900	+	1.02062i
$46$	−2.27939	−	5.11959i	−0.336078	−	0.754843i
$47$	−2.18126	−	10.2620i	−0.318169	−	1.49687i	−0.788862	−	0.614571i	$-0.789329\pi$
$47$	−2.18126	−	10.2620i	−0.318169	−	1.49687i	0.470692	−	0.882297i	$-0.344004\pi$
$48$	−0.152399	−	1.72533i	−0.0219970	−	0.249030i
$49$	4.61035	−	5.26732i	0.658621	−	0.752474i
$50$	2.09943	−	1.52532i	0.296904	−	0.215713i
$51$	−3.16675	+	2.22133i	−0.443434	+	0.311048i
$52$	−0.674863	+	0.607650i	−0.0935867	+	0.0842659i
$53$	1.15816	+	2.60126i	0.159085	+	0.357311i	0.975448	−	0.220228i	$-0.0706801\pi$
$53$	1.15816	+	2.60126i	0.159085	+	0.357311i	−0.816364	+	0.577538i	$0.804013\pi$
$54$	−0.799994	+	5.13420i	−0.108865	+	0.698676i
$55$	−1.65703	+	8.98886i	−0.223434	+	1.21206i
$56$	−0.295038	−	2.62925i	−0.0394261	−	0.351348i
$57$	−8.69025	+	7.56707i	−1.15105	+	1.00228i
$58$	4.28962	−	0.911786i	0.563254	−	0.119723i
$59$	−1.31314	+	6.17786i	−0.170957	+	0.804288i	0.806179	+	0.591672i	$0.201532\pi$
$59$	−1.31314	+	6.17786i	−0.170957	+	0.804288i	−0.977136	+	0.212617i	$0.931801\pi$
$60$	4.73828	+	0.577770i	0.611709	+	0.0745898i
$61$	1.19589	−	2.68601i	0.153118	−	0.343909i	−0.820657	−	0.571421i	$-0.806392\pi$
$61$	1.19589	−	2.68601i	0.153118	−	0.343909i	0.973775	+	0.227512i	$0.0730591\pi$
$62$	−0.0736192	−	0.226576i	−0.00934964	−	0.0287752i
$63$	−1.03625	+	7.86932i	−0.130555	+	0.991441i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.25135	−	2.16739i	−0.155210	−	0.268832i
$66$	−4.61165	+	3.42530i	−0.567655	+	0.421625i
$67$	2.80878	−	4.86495i	0.343147	−	0.594348i	−0.641868	−	0.766815i	$-0.721840\pi$
$67$	2.80878	−	4.86495i	0.343147	−	0.594348i	0.985015	+	0.172467i	$0.0551737\pi$
$68$	−0.233441	+	2.22105i	−0.0283089	+	0.269341i
$69$	8.32433	+	4.99230i	1.00213	+	0.601003i
$70$	7.25668	+	0.711193i	0.867339	+	0.0850038i
$71$	−2.57763	−	3.54780i	−0.305909	−	0.421047i	0.628191	−	0.778059i	$-0.283796\pi$
$71$	−2.57763	−	3.54780i	−0.305909	−	0.421047i	−0.934100	+	0.357012i	$0.883796\pi$
$72$	1.93220	+	2.29491i	0.227712	+	0.270458i
$73$	−2.21647	+	10.4277i	−0.259418	+	1.22047i	0.634744	+	0.772722i	$0.281105\pi$
$73$	−2.21647	+	10.4277i	−0.259418	+	1.22047i	−0.894162	+	0.447743i	$0.852228\pi$
$74$	7.25637	+	8.05901i	0.843536	+	0.936841i
$75$	−1.45979	+	4.25107i	−0.168562	+	0.490871i
$76$			6.65285i			0.763134i
$77$	−6.91874	+	5.39731i	−0.788464	+	0.615081i
$78$	0.352547	−	1.53289i	0.0399181	−	0.173565i
$79$	4.75825	+	0.500112i	0.535345	+	0.0562670i	0.368344	−	0.929690i	$-0.379925\pi$
$79$	4.75825	+	0.500112i	0.535345	+	0.0562670i	0.167001	+	0.985957i	$0.446592\pi$
$80$	2.04804	−	1.84406i	0.228978	−	0.206173i
$81$	−3.97235	−	8.07592i	−0.441372	−	0.897324i
$82$	−3.91141	−	1.74147i	−0.431943	−	0.192313i
$83$	3.07387	−	2.23330i	0.337402	−	0.245137i	−0.406163	−	0.913801i	$-0.633134\pi$
$83$	3.07387	−	2.23330i	0.337402	−	0.245137i	0.743565	+	0.668664i	$0.233134\pi$
$84$	3.03354	+	3.43477i	0.330986	+	0.374764i
$85$	−5.85348	−	1.90191i	−0.634899	−	0.206291i
$86$	−8.37800	−	0.880563i	−0.903423	−	0.0949535i
$87$	−5.17569	+	5.55956i	−0.554893	+	0.596047i
$88$	−0.257033	+	3.30665i	−0.0273998	+	0.352490i
$89$	−3.00107	+	1.73267i	−0.318112	+	0.183662i	−0.650551	−	0.759463i	$-0.725462\pi$
$89$	−3.00107	+	1.73267i	−0.318112	+	0.183662i	0.332439	+	0.943125i	$0.392129\pi$
$90$	−7.29347	+	3.89365i	−0.768800	+	0.410427i
$91$	0.483015	−	2.35360i	0.0506337	−	0.246725i
$92$	5.32981	−	1.73176i	0.555671	−	0.180548i
$93$	0.329755	+	0.248056i	0.0341940	+	0.0257222i
$94$	10.4338	−	1.09664i	1.07616	−	0.113109i
$95$	−17.9340	−	3.81199i	−1.83999	−	0.391101i
$96$	1.73181	+	0.0287819i	0.176752	+	0.00293754i
$97$	14.4550	+	10.5022i	1.46768	+	1.06633i	0.981277	+	0.192603i	$0.0616928\pi$
$97$	14.4550	+	10.5022i	1.46768	+	1.06633i	0.486407	+	0.873732i	$0.338307\pi$
$98$	4.75655	+	5.13568i	0.480484	+	0.518782i
$99$	3.13227	−	9.44399i	0.314805	−	0.949156i
$100$	1.29752	+	2.24736i	0.129752	+	0.224736i
$101$	13.8161	−	6.15131i	1.37475	−	0.612078i	0.419467	−	0.907770i	$-0.362217\pi$
$101$	13.8161	−	6.15131i	1.37475	−	0.612078i	0.955283	+	0.295692i	$0.0955502\pi$
$102$	−1.87814	−	3.38160i	−0.185964	−	0.334828i
$103$	−0.929037	+	1.03180i	−0.0915408	+	0.101666i	−0.787175	−	0.616730i	$-0.788457\pi$
$103$	−0.929037	+	1.03180i	−0.0915408	+	0.101666i	0.695634	+	0.718397i	$0.255124\pi$
$104$	−0.533779	−	0.734683i	−0.0523413	−	0.0720416i
$105$	−10.9972	+	6.20939i	−1.07322	+	0.605974i
$106$	−2.70807	+	0.879905i	−0.263031	+	0.0854640i
$107$	−3.96332	+	0.842430i	−0.383149	+	0.0814408i	−0.395459	−	0.918483i	$-0.629415\pi$
$107$	−3.96332	+	0.842430i	−0.383149	+	0.0814408i	0.0123107	+	0.999924i	$0.496081\pi$
$108$	−5.02245	−	1.33228i	−0.483286	−	0.128199i
$109$	0.347989	+	0.200911i	0.0333313	+	0.0192438i	0.516573	−	0.856243i	$-0.327207\pi$
$109$	0.347989	+	0.200911i	0.0333313	+	0.0192438i	−0.483242	+	0.875487i	$0.660541\pi$
$110$	−8.76641	−	2.58754i	−0.835845	−	0.246713i
$111$	−18.3053	−	4.21001i	−1.73746	−	0.399596i
$112$	2.64569	−	0.0185902i	0.249994	−	0.00175661i
$113$	17.6802	+	5.74465i	1.66321	+	0.540411i	0.981542	−	0.191247i	$-0.0612533\pi$
$113$	17.6802	+	5.74465i	1.66321	+	0.540411i	0.681672	+	0.731658i	$0.261253\pi$
$114$	−6.61724	−	9.43362i	−0.619762	−	0.883539i
$115$	1.61438	+	15.3598i	0.150541	+	1.43231i
$116$	0.458404	+	4.36142i	0.0425618	+	0.404948i
$117$	1.02478	+	2.52427i	0.0947409	+	0.233369i
$118$	−6.00675	−	1.95171i	−0.552966	−	0.179670i
$119$	−2.99023	−	5.09620i	−0.274114	−	0.467168i
$120$	−1.06989	+	4.65193i	−0.0976672	+	0.424661i
$121$	9.79143	−	5.01278i	0.890130	−	0.455707i
$122$	2.54629	+	1.47010i	0.230531	+	0.133097i
$123$	7.27846	−	1.42110i	0.656277	−	0.128136i
$124$	0.233031	−	0.0495322i	0.0209268	−	0.00444812i
$125$	6.30348	−	2.04812i	0.563800	−	0.183190i
$126$	−7.71789	−	1.85314i	−0.687564	−	0.165091i
$127$	−3.41705	−	4.70316i	−0.303214	−	0.417338i	0.630036	−	0.776566i	$-0.283040\pi$
$127$	−3.41705	−	4.70316i	−0.303214	−	0.417338i	−0.933250	+	0.359228i	$0.883040\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	12.7557	−	7.08454i	1.12308	−	0.623759i
$130$	2.28632	−	1.01794i	0.200524	−	0.0892789i
$131$	8.02200	+	13.8945i	0.700885	+	1.21397i	0.968156	+	0.250347i	$0.0805447\pi$
$131$	8.02200	+	13.8945i	0.700885	+	1.21397i	−0.267271	+	0.963621i	$0.586122\pi$
$132$	−2.92449	−	4.94443i	−0.254544	−	0.430357i
$133$	−10.4459	−	14.1671i	−0.905771	−	1.22844i
$134$	4.54470	+	3.30192i	0.392602	+	0.285242i
$135$	6.46920	−	12.7756i	0.556780	−	1.09955i
$136$	−2.18448	−	0.464325i	−0.187317	−	0.0398155i
$137$	9.04595	−	0.950767i	0.772848	−	0.0812295i	0.290108	−	0.956994i	$-0.406309\pi$
$137$	9.04595	−	0.950767i	0.772848	−	0.0812295i	0.482739	+	0.875764i	$0.339642\pi$
$138$	−5.83508	+	7.75689i	−0.496715	+	0.660310i
$139$	−15.7296	+	5.11087i	−1.33417	+	0.433498i	−0.887338	−	0.461119i	$-0.847448\pi$
$139$	−15.7296	+	5.11087i	−1.33417	+	0.433498i	−0.446832	+	0.894618i	$0.647448\pi$
$140$	−1.46583	+	7.14259i	−0.123885	+	0.603659i
$141$	−13.7042	+	11.9330i	−1.15410	+	1.00494i
$142$	3.79781	−	2.19266i	0.318705	−	0.184004i
$143$	−1.14992	+	2.78373i	−0.0961609	+	0.232787i
$144$	−2.48431	+	1.68173i	−0.207026	+	0.140144i
$145$	−12.0197	−	1.26332i	−0.998181	−	0.104913i
$146$	−10.1389	−	3.29431i	−0.839097	−	0.272639i
$147$	−11.8529	−	2.55121i	−0.977611	−	0.210420i
$148$	−8.77336	+	6.37422i	−0.721166	+	0.523958i
$149$	13.6840	+	6.09250i	1.12104	+	0.499117i	0.881696	−	0.471818i	$-0.156402\pi$
$149$	13.6840	+	6.09250i	1.12104	+	0.499117i	0.239340	+	0.970936i	$0.423069\pi$
$150$	−4.07519	−	1.89615i	−0.332738	−	0.154820i
$151$	−3.87172	+	3.48611i	−0.315076	+	0.283696i	−0.811461	−	0.584407i	$-0.801327\pi$
$151$	−3.87172	+	3.48611i	−0.315076	+	0.283696i	0.496385	+	0.868103i	$0.334661\pi$
$152$	−6.61640	−	0.695412i	−0.536661	−	0.0564053i
$153$	6.02667	+	2.92695i	0.487228	+	0.236630i
$154$	−4.64454	−	7.44501i	−0.374268	−	0.599936i
$155$			0.656558i			0.0527360i
$156$	1.48764	+	0.510846i	0.119107	+	0.0409004i
$157$	0.797111	+	0.885281i	0.0636164	+	0.0706532i	0.774113	−	0.633048i	$-0.218196\pi$
$157$	0.797111	+	0.885281i	0.0636164	+	0.0706532i	−0.710497	+	0.703701i	$0.751530\pi$
$158$	−0.994745	+	4.67991i	−0.0791377	+	0.372314i
$159$	2.96480	−	3.94127i	0.235124	−	0.312563i
$160$	1.61988	+	2.22958i	0.128063	+	0.176264i
$161$	−8.63061	+	12.0563i	−0.680188	+	0.950167i
$162$	8.44690	−	3.10642i	0.663651	−	0.244064i
$163$	−1.19889	+	11.4067i	−0.0939045	+	0.893441i	0.841594	+	0.540111i	$0.181618\pi$
$163$	−1.19889	+	11.4067i	−0.0939045	+	0.893441i	−0.935499	+	0.353331i	$0.885049\pi$
$164$	2.14079	−	3.70795i	0.167167	−	0.289542i
$165$	15.0043	−	5.05041i	1.16808	−	0.393174i
$166$	1.89976	+	3.29048i	0.147450	+	0.255391i
$167$	−13.4155	−	9.74696i	−1.03813	−	0.754243i	−0.0682071	−	0.997671i	$-0.521728\pi$
$167$	−13.4155	−	9.74696i	−1.03813	−	0.754243i	−0.969919	+	0.243429i	$0.921728\pi$
$168$	−3.73305	+	2.65789i	−0.288011	+	0.205060i
$169$	3.76238	+	11.5794i	0.289414	+	0.890725i
$170$	2.50335	−	5.62261i	0.191998	−	0.431235i
$171$	18.7663	+	6.79488i	1.43509	+	0.519617i
$172$	1.75148	−	8.24006i	0.133549	−	0.628298i
$173$	11.1481	−	2.36959i	0.847572	−	0.180157i	0.236401	−	0.971656i	$-0.424032\pi$
$173$	11.1481	−	2.36959i	0.847572	−	0.180157i	0.611171	+	0.791499i	$0.290699\pi$
$174$	−4.98809	−	5.72847i	−0.378146	−	0.434274i
$175$	−6.29170	−	2.74844i	−0.475608	−	0.207762i
$176$	−3.26167	−	0.601264i	−0.245858	−	0.0453220i
$177$	10.4587	−	3.20711i	0.786127	−	0.241061i
$178$	−1.40948	−	3.16574i	−0.105645	−	0.237282i
$179$	7.34748	−	6.61570i	0.549176	−	0.494481i	−0.347190	−	0.937795i	$-0.612864\pi$
$179$	7.34748	−	6.61570i	0.549176	−	0.494481i	0.896366	+	0.443314i	$0.146197\pi$
$180$	−3.10995	−	7.66052i	−0.231802	−	0.570981i
$181$	12.4958	−	9.07875i	0.928807	−	0.674818i	−0.0168932	−	0.999857i	$-0.505378\pi$
$181$	12.4958	−	9.07875i	0.928807	−	0.674818i	0.945701	+	0.325039i	$0.105378\pi$
$182$	2.29022	+	0.726387i	0.169762	+	0.0538434i
$183$	−5.07284	+	0.448086i	−0.374995	+	0.0331235i
$184$	1.16516	+	5.48163i	0.0858965	+	0.404111i
$185$	−12.1559	−	27.3026i	−0.893718	−	2.00732i
$186$	−0.281166	+	0.302019i	−0.0206161	+	0.0221451i
$187$	2.47922	+	6.97971i	0.181298	+	0.510407i
$188$			10.4913i			0.765155i
$189$	12.7871	−	5.04886i	0.930122	−	0.367251i
$190$	5.66571	−	17.4373i	0.411034	−	1.26503i
$191$	15.2558	+	13.7364i	1.10387	+	0.993932i	1.00000		0.000658696i	$-0.000209669\pi$
$191$	15.2558	+	13.7364i	1.10387	+	0.993932i	0.103873	+	0.994591i	$0.466876\pi$
$192$	−0.209648	+	1.71932i	−0.0151300	+	0.124081i
$193$	−23.7227	+	2.49336i	−1.70760	+	0.179476i	−0.907403	−	0.420263i	$-0.861938\pi$
$193$	−23.7227	+	2.49336i	−1.70760	+	0.179476i	−0.800196	+	0.599738i	$0.795271\pi$
$194$	−11.9556	+	13.2780i	−0.858363	+	0.953308i
$195$	−2.22948	+	3.71750i	−0.159656	+	0.266216i
$196$	−5.60474	+	4.19367i	−0.400339	+	0.299548i
$197$	−16.7596			−1.19407			−0.597037	−	0.802214i	$-0.703656\pi$
$197$	−16.7596			−1.19407			−0.597037	+	0.802214i	$0.703656\pi$
$198$	9.06484	+	4.10228i	0.644210	+	0.291536i
$199$	11.4850	−	19.8927i	0.814152	−	1.41015i	−0.0957828	−	0.995402i	$-0.530535\pi$
$199$	11.4850	−	19.8927i	0.814152	−	1.41015i	0.909935	−	0.414751i	$-0.136131\pi$
$200$	−2.37068	+	1.05550i	−0.167632	+	0.0746348i
$201$	−9.72855	−	0.161684i	−0.686199	−	0.0114043i
$202$	4.67344	+	14.3834i	0.328822	+	1.01201i
$203$	−7.82419	−	8.56780i	−0.549150	−	0.601342i
$204$	3.55939	−	1.51438i	0.249207	−	0.106028i
$205$	8.76882	+	7.89548i	0.612441	+	0.551445i
$206$	−0.929037	−	1.03180i	−0.0647291	−	0.0718889i
$207$	0.558669	−	16.8030i	0.0388302	−	1.16789i
$208$	0.786453	−	0.454059i	0.0545307	−	0.0314833i
$209$	9.51841	+	19.9064i	0.658402	+	1.37695i
$210$	−5.02585	−	11.5860i	−0.346816	−	0.799513i
$211$	14.6884	−	20.2169i	1.01119	−	1.39179i	0.0929963	−	0.995666i	$-0.470356\pi$
$211$	14.6884	−	20.2169i	1.01119	−	1.39179i	0.918198	−	0.396123i	$-0.129644\pi$
$212$	−0.592015	−	2.78521i	−0.0406597	−	0.191289i
$213$	−3.20429	+	6.88664i	−0.219555	+	0.471865i
$214$	−0.423535	−	4.02967i	−0.0289523	−	0.275462i
$215$	21.2090	+	9.44287i	1.44644	+	0.643998i
$216$	1.84997	−	4.85568i	0.125875	−	0.330387i
$217$	−0.418461	+	0.471367i	−0.0284070	+	0.0319985i
$218$	−0.236186	+	0.325082i	−0.0159965	+	0.0220173i
$219$	17.6534	−	5.41331i	1.19291	−	0.365798i
$220$	3.48971	−	8.44792i	0.235276	−	0.569558i
$221$	−1.75637	−	1.01404i	−0.118146	−	0.0682118i
$222$	6.10037	−	17.7649i	0.409430	−	1.19231i
$223$	−6.29557	+	19.3758i	−0.421582	+	1.29750i	0.484646	+	0.874710i	$0.338948\pi$
$223$	−6.29557	+	19.3758i	−0.421582	+	1.29750i	−0.906229	+	0.422787i	$0.861052\pi$
$224$	−0.258061	+	2.63314i	−0.0172424	+	0.175934i
$225$	7.66456	−	1.36467i	0.510970	−	0.0909783i
$226$	−7.56126	+	16.9829i	−0.502968	+	1.12968i
$227$	3.61620	+	0.768647i	0.240016	+	0.0510169i	0.326349	−	0.945249i	$-0.394182\pi$
$227$	3.61620	+	0.768647i	0.240016	+	0.0510169i	−0.0863331	+	0.996266i	$0.527515\pi$
$228$	10.0736	−	5.59491i	0.667143	−	0.370532i
$229$	1.37888	−	13.1192i	0.0911190	−	0.866940i	−0.849526	−	0.527547i	$-0.823112\pi$
$229$	1.37888	−	13.1192i	0.0911190	−	0.866940i	0.940645	−	0.339392i	$-0.110221\pi$
$230$	−15.4444			−1.01837
$231$	13.9910	+	5.93722i	0.920543	+	0.390640i
$232$	−4.38545			−0.287919
$233$	1.32065	−	12.5652i	0.0865188	−	0.823171i	−0.862098	−	0.506742i	$-0.830850\pi$
$233$	1.32065	−	12.5652i	0.0865188	−	0.823171i	0.948616	−	0.316429i	$-0.102484\pi$
$234$	−2.61756	+	0.755308i	−0.171115	+	0.0493760i
$235$	−28.2812	−	6.01135i	−1.84486	−	0.392137i
$236$	2.56890	−	5.76984i	0.167221	−	0.375584i
$237$	−3.24433	−	7.62545i	−0.210742	−	0.495326i
$238$	5.38085	−	2.44115i	0.348789	−	0.158237i
$239$	1.36443	−	4.19929i	0.0882578	−	0.271630i	−0.897180	−	0.441665i	$-0.854388\pi$
$239$	1.36443	−	4.19929i	0.0882578	−	0.271630i	0.985438	+	0.170035i	$0.0543881\pi$
$240$	−4.51461	−	1.55029i	−0.291417	−	0.100071i
$241$	−9.65705	−	5.57550i	−0.622065	−	0.359150i	0.155607	−	0.987819i	$-0.450267\pi$
$241$	−9.65705	−	5.57550i	−0.622065	−	0.359150i	−0.777673	+	0.628669i	$0.783600\pi$
$242$	3.96183	+	10.2618i	0.254676	+	0.659651i
$243$	−8.88776	+	12.8065i	−0.570150	+	0.821540i
$244$	−1.72821	+	2.37868i	−0.110637	+	0.152279i
$245$	−8.09338	−	17.5115i	−0.517067	−	1.11877i
$246$	0.652509	+	7.38713i	0.0416024	+	0.470987i
$247$	−5.51925	−	2.45733i	−0.351181	−	0.156356i
$248$	0.0249025	+	0.236932i	0.00158131	+	0.0150452i
$249$	−5.96669	−	2.77625i	−0.378124	−	0.175938i
$250$	1.37801	+	6.48303i	0.0871531	+	0.410023i
$251$	14.1993	−	19.5437i	0.896252	−	1.23359i	−0.0753957	−	0.997154i	$-0.524022\pi$
$251$	14.1993	−	19.5437i	0.896252	−	1.23359i	0.971648	−	0.236432i	$-0.0759780\pi$
$252$	2.64973	−	7.48191i	0.166917	−	0.471316i
$253$	13.4700	−	12.8072i	0.846849	−	0.805182i
$254$	5.03457	−	2.90671i	0.315897	−	0.182383i
$255$	2.04282	+	10.4627i	0.127926	+	0.655201i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−3.99776	−	3.59960i	−0.249373	−	0.224537i	0.534958	−	0.844878i	$-0.320327\pi$
$257$	−3.99776	−	3.59960i	−0.249373	−	0.224537i	−0.784332	+	0.620342i	$0.786994\pi$
$258$	5.71239	+	13.4264i	0.355638	+	0.835889i
$259$	8.67429	−	27.3491i	0.538994	−	1.69939i
$260$	0.773374	+	2.38020i	0.0479626	+	0.147614i
$261$	12.7708	+	3.16148i	0.790495	+	0.195691i
$262$	−14.6569	+	6.52568i	−0.905507	+	0.403158i
$263$	−6.87941	+	11.9155i	−0.424203	+	0.734740i	−0.996346	−	0.0854134i	$-0.972779\pi$
$263$	−6.87941	+	11.9155i	−0.424203	+	0.734740i	0.572143	+	0.820154i	$0.306112\pi$
$264$	5.22304	−	2.39163i	0.321456	−	0.147195i
$265$	7.84727			0.482054
$266$	15.1814	−	8.90778i	0.930830	−	0.546171i
$267$	5.14741	+	3.08703i	0.315016	+	0.188923i
$268$	−3.75888	+	4.17466i	−0.229610	+	0.255008i
$269$	6.29328	−	0.661450i	0.383708	−	0.0403293i	0.0892889	−	0.996006i	$-0.471541\pi$
$269$	6.29328	−	0.661450i	0.383708	−	0.0403293i	0.294419	+	0.955676i	$0.404874\pi$
$270$	12.0294	+	7.76918i	0.732084	+	0.472817i
$271$	1.69848	+	1.52932i	0.103175	+	0.0928996i	0.719104	−	0.694902i	$-0.244552\pi$
$271$	1.69848	+	1.52932i	0.103175	+	0.0928996i	−0.615929	+	0.787802i	$0.711219\pi$
$272$	0.690122	−	2.12398i	0.0418448	−	0.128785i
$273$	−3.96999	+	1.24796i	−0.240275	+	0.0755300i
$274$			9.09578i			0.549496i
$275$	7.09774	+	4.86808i	0.428010	+	0.293556i
$276$	−7.10447	−	6.61393i	−0.427639	−	0.398112i
$277$	−3.73663	−	8.39261i	−0.224512	−	0.504263i	0.765807	−	0.643071i	$-0.222340\pi$
$277$	−3.73663	−	8.39261i	−0.224512	−	0.504263i	−0.990319	+	0.138807i	$0.955673\pi$
$278$	−3.43868	−	16.1777i	−0.206238	−	0.970274i
$279$	0.0982858	−	0.707919i	0.00588422	−	0.0423820i
$280$	−6.95024	−	2.20440i	−0.415356	−	0.131738i
$281$	−5.24984	+	3.81423i	−0.313179	+	0.227538i	−0.733259	−	0.679949i	$-0.762002\pi$
$281$	−5.24984	+	3.81423i	−0.313179	+	0.227538i	0.420080	+	0.907487i	$0.362002\pi$
$282$	−10.4351	−	14.8764i	−0.621403	−	0.885879i
$283$	−4.90246	+	4.41420i	−0.291421	+	0.262397i	−0.801853	−	0.597521i	$-0.796152\pi$
$283$	−4.90246	+	4.41420i	−0.291421	+	0.262397i	0.510432	+	0.859918i	$0.329486\pi$
$284$	1.78367	+	4.00620i	0.105842	+	0.237724i
$285$	9.31007	+	30.3611i	0.551481	+	1.79844i
$286$	−2.64828	−	1.43460i	−0.156596	−	0.0848295i
$287$	1.26323	+	11.2573i	0.0745658	+	0.664498i
$288$	−1.41284	−	2.64649i	−0.0832523	−	0.155946i
$289$	11.7500	−	2.49753i	0.691174	−	0.146914i
$290$	2.51280	−	11.8218i	0.147557	−	0.694199i
$291$	3.74586	−	30.7197i	0.219586	−	1.80082i
$292$	4.33606	−	9.73896i	0.253749	−	0.569929i
$293$	3.95822	+	12.1821i	0.231241	+	0.711688i	0.997598	+	0.0692722i	$0.0220677\pi$
$293$	3.95822	+	12.1821i	0.231241	+	0.711688i	−0.766356	+	0.642416i	$0.777932\pi$
$294$	3.77620	−	11.5213i	0.220232	−	0.671936i
$295$	14.0817	+	10.2310i	0.819870	+	0.595670i
$296$	−5.42224	−	9.39159i	−0.315161	−	0.545875i
$297$	−16.9341	+	3.19936i	−0.982617	+	0.185646i
$298$	−7.48949	+	12.9722i	−0.433855	+	0.751459i
$299$	−0.531964	+	5.06130i	−0.0307643	+	0.292703i
$300$	2.31174	−	3.85467i	0.133468	−	0.222549i
$301$	9.20827	+	20.2971i	0.530756	+	1.16990i
$302$	−3.06231	−	4.21491i	−0.176216	−	0.242541i
$303$	−20.9333	−	15.7469i	−1.20258	−	0.904638i
$304$	1.38320	−	6.50747i	0.0793322	−	0.373229i
$305$	−5.42193	−	6.02166i	−0.310459	−	0.344799i
$306$	−3.54088	+	5.68771i	−0.202418	+	0.325145i
$307$		−	13.7899i		−	0.787032i	−0.919318	−	0.393516i	$-0.871259\pi$
$307$		−	13.7899i		−	0.787032i	0.919318	−	0.393516i	$-0.128741\pi$
$308$	7.88972	−	3.84088i	0.449558	−	0.218855i
$309$	2.34364	+	0.539010i	0.133325	+	0.0306632i
$310$	−0.652962	−	0.0686290i	−0.0370857	−	0.00389787i
$311$	−22.7419	+	20.4769i	−1.28957	+	1.16114i	−0.312105	+	0.950048i	$0.601034\pi$
$311$	−22.7419	+	20.4769i	−1.28957	+	1.16114i	−0.977467	+	0.211089i	$0.932299\pi$
$312$	−0.663548	+	1.42609i	−0.0375660	+	0.0807366i
$313$	−9.47181	−	4.21712i	−0.535379	−	0.238366i	0.121194	−	0.992629i	$-0.461328\pi$
$313$	−9.47181	−	4.21712i	−0.535379	−	0.238366i	−0.656572	+	0.754263i	$0.727994\pi$
$314$	−0.963753	+	0.700207i	−0.0543877	+	0.0395150i
$315$	18.6506	+	11.4299i	1.05084	+	0.644000i
$316$	−4.55029	−	1.47848i	−0.255974	−	0.0831710i
$317$	−23.2914	−	2.44802i	−1.30817	−	0.137495i	−0.575347	−	0.817910i	$-0.695133\pi$
$317$	−23.2914	−	2.44802i	−1.30817	−	0.137495i	−0.732827	+	0.680415i	$0.761800\pi$
$318$	3.60977	+	3.36053i	0.202426	+	0.188449i
$319$	7.61163	+	12.3942i	0.426169	+	0.693943i
$320$	−2.38669	+	1.37795i	−0.133420	+	0.0770300i
$321$	4.60867	+	5.29273i	0.257231	+	0.295411i
$322$	−11.0881	−	9.84356i	−0.617914	−	0.548560i
$323$	−14.1305	+	4.59127i	−0.786241	+	0.255465i
$324$	2.20646	+	8.72534i	0.122581	+	0.484741i
$325$	−2.34369	+	0.246331i	−0.130004	+	0.0136640i
$326$	−11.2189	−	2.38465i	−0.621357	−	0.132073i
$327$	0.0115652	−	0.695882i	0.000639558	−	0.0384823i
$328$	3.46386	+	2.51664i	0.191260	+	0.138958i
$329$	−16.4727	−	22.3409i	−0.908170	−	1.23170i
$330$	3.45436	+	15.4500i	0.190156	+	0.850496i
$331$	5.45074	+	9.44095i	0.299600	+	0.518922i	0.976044	−	0.217572i	$-0.0698136\pi$
$331$	5.45074	+	9.44095i	0.299600	+	0.518922i	−0.676445	+	0.736493i	$0.736480\pi$
$332$	−3.47103	+	1.54540i	−0.190498	+	0.0848150i
$333$	9.01966	+	31.2581i	0.494274	+	1.71293i
$334$	11.0959	−	12.3232i	0.607139	−	0.674296i
$335$	−9.09979	−	12.5248i	−0.497174	−	0.684302i
$336$	−2.25312	−	3.99042i	−0.122918	−	0.217695i
$337$	−24.0108	+	7.80159i	−1.30795	+	0.424979i	−0.878341	−	0.478034i	$-0.841349\pi$
$337$	−24.0108	+	7.80159i	−1.30795	+	0.424979i	−0.429611	+	0.903014i	$0.641349\pi$
$338$	−11.9093	+	2.53139i	−0.647778	+	0.137690i
$339$	−6.17025	−	31.6022i	−0.335122	−	1.71640i
$340$	5.33014	+	3.07736i	0.289067	+	0.166893i
$341$	0.626397	−	0.481611i	0.0339213	−	0.0260807i
$342$	−8.71927	+	17.9532i	−0.471484	+	0.970798i
$343$	5.35054	−	17.7305i	0.288902	−	0.957359i
$344$	8.01184	+	2.60320i	0.431969	+	0.140355i
$345$	21.8998	−	15.3617i	1.17905	−	0.827047i
$346$	1.19132	+	11.3347i	0.0640459	+	0.609356i
$347$	−0.936447	−	8.90970i	−0.0502711	−	0.478298i	−0.990476	−	0.137688i	$-0.956033\pi$
$347$	−0.936447	−	8.90970i	−0.0502711	−	0.478298i	0.940205	−	0.340610i	$-0.110634\pi$
$348$	6.21849	−	4.36198i	0.333346	−	0.233827i
$349$	−3.82596	−	1.24313i	−0.204799	−	0.0665433i	0.204821	−	0.978799i	$-0.434339\pi$
$349$	−3.82596	−	1.24313i	−0.204799	−	0.0665433i	−0.409620	+	0.912256i	$0.634339\pi$
$350$	3.39104	−	5.96994i	0.181259	−	0.319107i
$351$	2.96039	−	3.67456i	0.158014	−	0.196134i
$352$	0.938908	−	3.18095i	0.0500439	−	0.169545i
$353$	−20.7273	−	11.9669i	−1.10320	−	0.636935i	−0.166143	−	0.986102i	$-0.553131\pi$
$353$	−20.7273	−	11.9669i	−1.10320	−	0.636935i	−0.937061	+	0.349167i	$0.886465\pi$
$354$	2.09631	+	10.7367i	0.111417	+	0.570648i
$355$	−11.8215	+	2.51273i	−0.627418	+	0.133362i
$356$	3.29573	−	1.07085i	0.174673	−	0.0567548i
$357$	−5.20186	+	8.81357i	−0.275312	+	0.466463i
$358$	5.81144	+	7.99876i	0.307144	+	0.422748i
$359$	−17.7065	+	19.6650i	−0.934512	+	1.03788i	0.0646884	+	0.997906i	$0.479395\pi$
$359$	−17.7065	+	19.6650i	−0.934512	+	1.03788i	−0.999201	+	0.0399755i	$0.987272\pi$
$360$	7.94363	−	2.29217i	0.418666	−	0.120808i
$361$	−23.0765	+	10.2743i	−1.21455	+	0.540753i
$362$	7.72284	+	13.3764i	0.405904	+	0.703046i
$363$	−15.8247	−	10.6104i	−0.830579	−	0.556900i
$364$	−0.961801	+	2.20175i	−0.0504121	+	0.115403i
$365$	23.7687	+	17.2689i	1.24411	+	0.903898i
$366$	0.0846246	−	5.09188i	0.00442340	−	0.266157i
$367$	−9.15707	−	1.94640i	−0.477995	−	0.101601i	−0.0373877	−	0.999301i	$-0.511904\pi$
$367$	−9.15707	−	1.94640i	−0.477995	−	0.101601i	−0.440608	+	0.897700i	$0.645237\pi$
$368$	−5.57339	+	0.585787i	−0.290533	+	0.0305363i
$369$	−8.27285	−	9.82581i	−0.430667	−	0.511511i
$370$	28.4236	−	9.23540i	1.47767	−	0.480126i
$371$	5.63384	+	5.00150i	0.292494	+	0.259665i
$372$	−0.270975	−	0.311196i	−0.0140494	−	0.0161347i
$373$	−21.2488	+	12.2680i	−1.10022	+	0.635214i	−0.936279	−	0.351256i	$-0.885755\pi$
$373$	−21.2488	+	12.2680i	−1.10022	+	0.635214i	−0.163943	+	0.986470i	$0.552421\pi$
$374$	−7.20063	+	1.73606i	−0.372336	+	0.0897694i
$375$	−8.40234	−	7.82219i	−0.433895	−	0.403936i
$376$	−10.4338	−	1.09664i	−0.538082	−	0.0565547i
$377$	−3.78759	−	1.23066i	−0.195071	−	0.0633823i
$378$	3.68459	+	13.2448i	0.189515	+	0.681237i
$379$	−19.2969	+	14.0200i	−0.991217	+	0.720161i	−0.960187	−	0.279357i	$-0.909879\pi$
$379$	−19.2969	+	14.0200i	−0.991217	+	0.720161i	−0.0310297	+	0.999518i	$0.509879\pi$
$380$	16.7495	+	7.45737i	0.859232	+	0.382555i
$381$	−4.24778	+	9.12930i	−0.217620	+	0.467708i
$382$	−15.2558	+	13.7364i	−0.780556	+	0.702816i
$383$	19.3608	+	2.03491i	0.989293	+	0.103979i	0.585329	−	0.810796i	$-0.300965\pi$
$383$	19.3608	+	2.03491i	0.989293	+	0.103979i	0.403964	+	0.914775i	$0.367632\pi$
$384$	−1.68798	−	0.388217i	−0.0861395	−	0.0198111i
$385$	5.83311	+	23.4690i	0.297283	+	1.19609i
$386$		−	23.8534i		−	1.21411i
$387$	−21.4546	−	13.3565i	−1.09060	−	0.678950i
$388$	−11.9556	−	13.2780i	−0.606954	−	0.674091i
$389$	3.11706	−	14.6646i	0.158041	−	0.743526i	−0.825725	−	0.564073i	$-0.809234\pi$
$389$	3.11706	−	14.6646i	0.158041	−	0.743526i	0.983766	−	0.179454i	$-0.0574330\pi$
$390$	−3.46409	−	2.60585i	−0.175411	−	0.131952i
$391$	7.35643	+	10.1253i	0.372031	+	0.512056i
$392$	−3.58484	−	6.01240i	−0.181062	−	0.303672i
$393$	14.2925	−	23.8318i	0.720961	−	1.20215i
$394$	1.75186	−	16.6678i	0.0882574	−	0.839713i
$395$	6.59277	−	11.4190i	0.331718	−	0.574553i
$396$	−5.02734	+	8.58638i	−0.252633	+	0.431482i
$397$	12.3184	+	21.3361i	0.618243	+	1.07083i	0.989806	+	0.142421i	$0.0454887\pi$
$397$	12.3184	+	21.3361i	0.618243	+	1.07083i	−0.371563	+	0.928408i	$0.621178\pi$
$398$	18.5832	+	13.5015i	0.931490	+	0.676767i
$399$	−12.6668	+	27.7312i	−0.634134	+	1.38830i
$400$	−0.801909	−	2.46802i	−0.0400955	−	0.123401i
$401$	9.87635	−	22.1827i	0.493202	−	1.10775i	−0.479890	−	0.877329i	$-0.659323\pi$
$401$	9.87635	−	22.1827i	0.493202	−	1.10775i	0.973091	−	0.230420i	$-0.0740100\pi$
$402$	1.17771	−	9.65836i	0.0587388	−	0.481715i
$403$	−0.0449811	+	0.211619i	−0.00224067	+	0.0105415i
$404$	−14.7931	+	3.14437i	−0.735984	+	0.156438i
$405$	−24.7850	+	0.948437i	−1.23158	+	0.0471282i
$406$	9.33872	−	6.88575i	0.463473	−	0.341734i
$407$	−17.1315	+	31.6250i	−0.849178	+	1.56759i
$408$	1.13403	+	3.69819i	0.0561428	+	0.183088i
$409$	10.9353	+	24.5611i	0.540715	+	1.21447i	0.952877	+	0.303356i	$0.0981070\pi$
$409$	10.9353	+	24.5611i	0.540715	+	1.21447i	−0.412162	+	0.911110i	$0.635226\pi$
$410$	−8.76882	+	7.89548i	−0.433061	+	0.389930i
$411$	−9.04710	−	12.8977i	−0.446260	−	0.636194i
$412$	1.12326	−	0.816095i	0.0553390	−	0.0402061i
$413$	3.58901	+	16.3203i	0.176604	+	0.803067i
$414$	16.6525	+	2.31200i	0.818428	+	0.113629i
$415$	−2.17707	−	10.2423i	−0.106868	−	0.502775i
$416$	0.369365	+	0.829607i	0.0181096	+	0.0406748i
$417$	20.9671	+	19.5194i	1.02676	+	0.955870i
$418$	−20.7923	+	7.38549i	−1.01698	+	0.361236i
$419$		−	9.11719i		−	0.445404i	−0.974887	−	0.222702i	$-0.928512\pi$
$419$		−	9.11719i		−	0.445404i	0.974887	−	0.222702i	$-0.0714877\pi$
$420$	12.0479	−	3.78724i	0.587879	−	0.184799i
$421$	−5.30508	+	16.3274i	−0.258554	+	0.795747i	0.734555	+	0.678550i	$0.237391\pi$
$421$	−5.30508	+	16.3274i	−0.258554	+	0.795747i	−0.993109	+	0.117198i	$0.962609\pi$
$422$	18.5708	+	16.7212i	0.904012	+	0.813976i
$423$	29.5937	+	10.7153i	1.43889	+	0.520993i
$424$	2.83184	−	0.297638i	0.137526	−	0.0144546i
$425$	−3.87790	+	4.30685i	−0.188106	+	0.208913i
$426$	−6.51397	−	3.90659i	−0.315603	−	0.189275i
$427$	−0.0546591	−	7.77886i	−0.00264514	−	0.376446i
$428$	4.05186			0.195854
$429$	5.18214	−	0.599875i	0.250196	−	0.0289623i
$430$	−11.6081	+	20.1058i	−0.559792	+	0.969588i
$431$	35.8153	−	15.9460i	1.72516	−	0.768092i	0.728629	−	0.684909i	$-0.240158\pi$
$431$	35.8153	−	15.9460i	1.72516	−	0.768092i	0.996534	−	0.0831836i	$-0.0265088\pi$
$432$	4.63570	+	2.34739i	0.223035	+	0.112939i
$433$	−2.30058	−	7.08046i	−0.110559	−	0.340265i	0.880436	−	0.474165i	$-0.157250\pi$
$433$	−2.30058	−	7.08046i	−0.110559	−	0.340265i	−0.990995	+	0.133900i	$0.957250\pi$
$434$	−0.425044	−	0.465440i	−0.0204028	−	0.0223418i
$435$	8.19542	+	19.2624i	0.392940	+	0.923564i
$436$	−0.298613	−	0.268872i	−0.0143010	−	0.0128766i
$437$	24.9473	+	27.7068i	1.19339	+	1.32540i
$438$	3.53838	+	18.1225i	0.169070	+	0.865928i
$439$	24.1794	−	13.9600i	1.15402	−	0.666273i	0.204155	−	0.978939i	$-0.434555\pi$
$439$	24.1794	−	13.9600i	1.15402	−	0.666273i	0.949863	+	0.312666i	$0.101222\pi$
$440$	8.03686	+	4.35364i	0.383142	+	0.207552i
$441$	6.10506	+	20.0930i	0.290717	+	0.956809i
$442$	1.19208	−	1.64075i	0.0567013	−	0.0780427i
$443$	1.21132	+	5.69881i	0.0575516	+	0.270759i	0.997510	−	0.0705313i	$-0.0224695\pi$
$443$	1.21132	+	5.69881i	0.0575516	+	0.270759i	−0.939958	+	0.341290i	$0.889136\pi$
$444$	17.0300	+	7.92389i	0.808206	+	0.376051i
$445$	0.998261	+	9.49782i	0.0473221	+	0.450240i
$446$	−18.6116	−	8.28640i	−0.881283	−	0.392372i
$447$	−2.28279	−	25.8437i	−0.107972	−	1.22237i
$448$	−2.59174	−	0.531885i	−0.122448	−	0.0251292i
$449$	−6.92207	+	9.52742i	−0.326673	+	0.449627i	−0.940490	−	0.339822i	$-0.889633\pi$
$449$	−6.92207	+	9.52742i	−0.326673	+	0.449627i	0.613817	+	0.789448i	$0.289633\pi$
$450$	0.556035	+	7.76522i	0.0262117	+	0.366056i
$451$	1.10051	−	14.1577i	0.0518208	−	0.666658i
$452$	−16.0995	−	9.29503i	−0.757255	−	0.437202i
$453$	8.53466	+	2.93075i	0.400993	+	0.137698i
$454$	−1.14243	+	3.51604i	−0.0536170	+	0.165016i
$455$	−5.38412	−	3.85428i	−0.252411	−	0.180692i
$456$	4.51128	+	10.6033i	0.211260	+	0.496544i
$457$	−12.2727	+	27.5649i	−0.574092	+	1.28943i	0.360185	+	0.932881i	$0.382714\pi$
$457$	−12.2727	+	27.5649i	−0.574092	+	1.28943i	−0.934276	+	0.356550i	$0.883953\pi$
$458$	12.9032	+	2.74265i	0.602926	+	0.128156i
$459$	−0.636369	−	11.5870i	−0.0297032	−	0.540835i
$460$	1.61438	−	15.3598i	0.0752707	−	0.716153i
$461$	−11.0690			−0.515533			−0.257767	−	0.966207i	$-0.582987\pi$
$461$	−11.0690			−0.515533			−0.257767	+	0.966207i	$0.582987\pi$
$462$	−7.36715	+	13.2938i	−0.342751	+	0.618483i
$463$	2.93172			0.136249			0.0681243	−	0.997677i	$-0.478299\pi$
$463$	2.93172			0.136249			0.0681243	+	0.997677i	$0.478299\pi$
$464$	0.458404	−	4.36142i	0.0212809	−	0.202474i
$465$	0.994150	−	0.552152i	0.0461026	−	0.0256055i
$466$	12.3583	+	2.62683i	0.572486	+	0.121686i
$467$	14.5556	−	32.6924i	0.673552	−	1.51282i	−0.175480	−	0.984483i	$-0.556148\pi$
$467$	14.5556	−	32.6924i	0.673552	−	1.51282i	0.849033	−	0.528341i	$-0.177186\pi$
$468$	−0.477561	−	2.68217i	−0.0220753	−	0.123983i
$469$	1.44967	−	14.7918i	0.0669397	−	0.683022i
$470$	8.93461	−	27.4979i	0.412123	−	1.26838i
$471$	0.670124	−	1.95148i	0.0308777	−	0.0899193i
$472$	5.46971	+	3.15794i	0.251764	+	0.145356i
$473$	−6.54858	−	27.1615i	−0.301104	−	1.24888i
$474$	7.92280	−	2.42948i	0.363906	−	0.111590i
$475$	−10.1477	+	13.9672i	−0.465610	+	0.640857i
$476$	1.86533	+	5.60654i	0.0854973	+	0.256975i
$477$	−8.46114	−	1.17472i	−0.387409	−	0.0537869i
$478$	4.03367	+	1.79590i	0.184496	+	0.0821427i
$479$	2.02764	+	19.2917i	0.0926454	+	0.881462i	0.937855	+	0.347027i	$0.112809\pi$
$479$	2.02764	+	19.2917i	0.0926454	+	0.881462i	−0.845210	+	0.534435i	$0.820525\pi$
$480$	2.01370	−	4.32783i	0.0919124	−	0.197537i
$481$	−2.04753	−	9.63286i	−0.0933592	−	0.439221i
$482$	6.55440	−	9.02135i	0.298545	−	0.410911i
$483$	25.5136	+	2.92926i	1.16091	+	0.133286i
$484$	−10.6197	+	2.86748i	−0.482713	+	0.130340i
$485$	42.6438	−	24.6204i	1.93636	−	1.11796i
$486$	−11.8074	−	10.1777i	−0.535593	−	0.461671i
$487$	−5.39572	−	5.99255i	−0.244503	−	0.271548i	0.608385	−	0.793642i	$-0.291818\pi$
$487$	−5.39572	−	5.99255i	−0.244503	−	0.271548i	−0.852888	+	0.522094i	$0.825151\pi$
$488$	−2.18500	−	1.96738i	−0.0989103	−	0.0890592i
$489$	18.2801	−	7.77746i	0.826654	−	0.351709i
$490$	18.2616	−	6.21859i	0.824975	−	0.280927i
$491$	8.27669	+	25.4730i	0.373522	+	1.14958i	0.944470	+	0.328597i	$0.106576\pi$
$491$	8.27669	+	25.4730i	0.373522	+	1.14958i	−0.570948	+	0.820986i	$0.693424\pi$
$492$	−7.41487	−	0.123232i	−0.334288	−	0.00555571i
$493$	−8.94720	+	3.98355i	−0.402962	+	0.179410i
$494$	3.02079	−	5.23215i	0.135912	−	0.235406i
$495$	−20.2656	−	18.4720i	−0.910870	−	0.830255i
$496$	−0.238237			−0.0106971
$497$	−10.0886	−	5.73050i	−0.452534	−	0.257048i
$498$	3.38473	−	5.64381i	0.151673	−	0.252905i
$499$	−6.22535	+	6.91395i	−0.278685	+	0.309511i	−0.866195	−	0.499706i	$-0.833441\pi$
$499$	−6.22535	+	6.91395i	−0.278685	+	0.309511i	0.587510	+	0.809217i	$0.300108\pi$
$500$	−6.59156	+	0.692801i	−0.294784	+	0.0309830i
$501$	−3.47649	+	28.5106i	−0.155318	+	1.27376i
$502$	17.9524	+	16.1644i	0.801254	+	0.721452i
$503$	−1.28741	+	3.96225i	−0.0574029	+	0.176668i	−0.975647	−	0.219347i	$-0.929607\pi$
$503$	−1.28741	+	3.96225i	−0.0574029	+	0.176668i	0.918244	+	0.396015i	$0.129607\pi$
$504$	7.16395	+	3.41729i	0.319108	+	0.152218i
$505$		−	41.6792i		−	1.85470i
$506$	11.3291	+	14.7349i	0.503638	+	0.655046i
$507$	14.3693	−	15.4350i	0.638162	−	0.685492i
$508$	2.36453	+	5.31083i	0.104909	+	0.235630i
$509$	3.84990	+	18.1123i	0.170644	+	0.802815i	0.977311	+	0.211809i	$0.0679356\pi$
$509$	3.84990	+	18.1123i	0.170644	+	0.802815i	−0.806667	+	0.591006i	$0.798731\pi$
$510$	−10.6189	+	0.937975i	−0.470214	+	0.0415342i
$511$	6.05793	+	27.5471i	0.267987	+	1.21861i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−5.49336	−	34.1299i	−0.242538	−	1.50687i
$514$	3.99776	−	3.59960i	0.176334	−	0.158771i
$515$	1.55633	+	3.49556i	0.0685799	+	0.154033i
$516$	−13.9499	+	4.27766i	−0.614111	+	0.188314i
$517$	15.0102	+	31.3916i	0.660146	+	1.38060i
$518$	26.2926	+	11.4855i	1.15523	+	0.504646i
$519$	−12.9633	−	14.8874i	−0.569026	−	0.653486i
$520$	−2.44800	+	0.520339i	−0.107352	+	0.0228184i
$521$	2.41312	−	11.3528i	0.105721	−	0.497377i	−0.893145	−	0.449768i	$-0.851507\pi$
$521$	2.41312	−	11.3528i	0.105721	−	0.497377i	0.998866	−	0.0476089i	$-0.0151601\pi$
$522$	−4.47908	+	12.3704i	−0.196044	+	0.541439i
$523$	−3.45369	+	7.75711i	−0.151019	+	0.339195i	−0.973174	−	0.230069i	$-0.926105\pi$
$523$	−3.45369	+	7.75711i	−0.151019	+	0.339195i	0.822155	+	0.569263i	$0.192772\pi$
$524$	−4.95787	−	15.2587i	−0.216585	−	0.666581i
$525$	1.12955	+	11.8382i	0.0492978	+	0.516660i
$526$	−11.1311	−	8.08723i	−0.485340	−	0.352620i
$527$	0.266025	+	0.460768i	0.0115882	+	0.0200714i
$528$	1.83257	+	5.44442i	0.0797525	+	0.236938i
$529$	4.20293	−	7.27968i	0.182736	−	0.316508i
$530$	−0.820263	+	7.80428i	−0.0356299	+	0.338996i
$531$	−13.6517	−	13.1393i	−0.592435	−	0.570199i
$532$	7.27210	+	16.0293i	0.315285	+	0.694959i
$533$	2.28541	+	3.14560i	0.0989921	+	0.136251i
$534$	−3.60817	+	4.79653i	−0.156141	+	0.207566i
$535$	−2.32166	+	10.9226i	−0.100374	+	0.472223i
$536$	−3.75888	−	4.17466i	−0.162359	−	0.180318i
$537$	−16.1965	−	5.56176i	−0.698929	−	0.240008i
$538$			6.32794i			0.272817i
$539$	−10.7703	+	20.5670i	−0.463909	+	0.885883i
$540$	−8.98403	+	11.1514i	−0.386611	+	0.479879i
$541$	−39.5292	−	4.15468i	−1.69949	−	0.178624i	−0.795436	−	0.606038i	$-0.792758\pi$
$541$	−39.5292	−	4.15468i	−1.69949	−	0.178624i	−0.904056	+	0.427414i	$0.859425\pi$
$542$	−1.69848	+	1.52932i	−0.0729560	+	0.0656899i
$543$	−24.2556	−	11.2859i	−1.04091	−	0.484326i
$544$	2.04020	+	0.908357i	0.0874730	+	0.0389455i
$545$	0.895895	−	0.650906i	0.0383759	−	0.0278818i
$546$	−0.826147	−	4.07869i	−0.0353558	−	0.174552i
$547$	−8.50536	−	2.76356i	−0.363663	−	0.118161i	0.121485	−	0.992593i	$-0.461234\pi$
$547$	−8.50536	−	2.76356i	−0.363663	−	0.118161i	−0.485148	+	0.874432i	$0.661234\pi$
$548$	−9.04595	−	0.950767i	−0.386424	−	0.0406148i
$549$	4.94464	+	7.30437i	0.211032	+	0.311743i
$550$	−5.58333	+	6.55001i	−0.238074	+	0.279293i
$551$	−25.2669	+	14.5879i	−1.07641	+	0.621464i
$552$	7.32032	−	6.37420i	0.311574	−	0.271304i
$553$	12.0112	−	3.99618i	0.510766	−	0.169935i
$554$	8.73722	−	2.83890i	0.371209	−	0.120613i
$555$	−31.1182	+	41.3672i	−1.32090	+	1.75594i
$556$	16.4485	−	1.72881i	0.697572	−	0.0733178i
$557$	14.2055	+	3.01946i	0.601904	+	0.127939i	0.498778	−	0.866730i	$-0.333782\pi$
$557$	14.2055	+	3.01946i	0.601904	+	0.127939i	0.103126	+	0.994668i	$0.467115\pi$
$558$	0.693768	+	0.171745i	0.0293695	+	0.00727055i
$559$	6.18908	+	4.49663i	0.261770	+	0.190187i
$560$	2.91882	−	6.68174i	0.123343	−	0.282355i
$561$	8.48360	−	9.62379i	0.358178	−	0.406317i
$562$	−3.24458	−	5.61977i	−0.136864	−	0.237056i
$563$	−31.7810	+	14.1498i	−1.33941	+	0.596344i	−0.946343	−	0.323165i	$-0.895253\pi$
$563$	−31.7810	+	14.1498i	−1.33941	+	0.596344i	−0.393069	+	0.919509i	$0.628587\pi$
$564$	15.8857	−	8.82295i	0.668909	−	0.371513i
$565$	34.2812	−	38.0732i	1.44222	−	1.60175i
$566$	−3.87757	−	5.33702i	−0.162986	−	0.224331i
$567$	−18.3986	−	15.1160i	−0.772667	−	0.634811i
$568$	−4.17069	+	1.35514i	−0.174998	+	0.0568604i
$569$	−39.3585	+	8.36592i	−1.65000	+	0.350717i	−0.936697	−	0.350142i	$-0.886133\pi$
$569$	−39.3585	+	8.36592i	−1.65000	+	0.350717i	−0.713299	+	0.700859i	$0.752800\pi$
$570$	−31.1680	+	6.08547i	−1.30548	+	0.254892i
$571$	13.0787	+	7.55102i	0.547328	+	0.316000i	0.748044	−	0.663649i	$-0.230993\pi$
$571$	13.0787	+	7.55102i	0.547328	+	0.316000i	−0.200715	+	0.979650i	$0.564327\pi$
$572$	1.70356	−	2.48382i	0.0712294	−	0.103854i
$573$	7.96960	−	34.6522i	0.332935	−	1.44762i
$574$	−11.3277	+	0.0795954i	−0.472809	+	0.00332225i
$575$	13.8310	+	4.49397i	0.576794	+	0.187412i
$576$	2.77967	−	1.12847i	0.115820	−	0.0470194i
$577$	−1.60227	−	15.2446i	−0.0667034	−	0.634640i	−0.975892	−	0.218255i	$-0.929964\pi$
$577$	−1.60227	−	15.2446i	−0.0667034	−	0.634640i	0.909188	−	0.416385i	$-0.136703\pi$
$578$	1.25564	+	11.9467i	0.0522279	+	0.496915i
$579$	23.7257	+	33.8237i	0.986008	+	1.40566i
$580$	11.4944	+	3.73475i	0.477278	+	0.155077i
$581$	4.96499	−	8.74089i	0.205983	−	0.362633i
$582$	30.1598	+	6.93642i	1.25017	+	0.287524i
$583$	−5.75628	−	7.48678i	−0.238401	−	0.310071i
$584$	9.23237	+	5.33031i	0.382038	+	0.220570i
$585$	7.50393	+	0.249492i	0.310249	+	0.0103152i
$586$	−12.5291	+	2.66315i	−0.517574	+	0.110014i
$587$	−5.75326	+	1.86935i	−0.237462	+	0.0771562i	−0.425331	−	0.905038i	$-0.639842\pi$
$587$	−5.75326	+	1.86935i	−0.237462	+	0.0771562i	0.187868	+	0.982194i	$0.439842\pi$
$588$	11.0635	+	4.95981i	0.456250	+	0.204539i
$589$	0.931611	+	1.28225i	0.0383864	+	0.0528343i
$590$	−11.6469	+	12.9352i	−0.479494	+	0.532532i
$591$	14.0945	+	25.3772i	0.579771	+	1.04388i
$592$	9.90692	−	4.41084i	0.407172	−	0.181285i
$593$	−6.96755	−	12.0681i	−0.286123	−	0.495579i	0.686758	−	0.726886i	$-0.259033\pi$
$593$	−6.96755	−	12.0681i	−0.286123	−	0.495579i	−0.972881	+	0.231307i	$0.925700\pi$
$594$	−1.41174	−	17.1758i	−0.0579244	−	0.704730i
$595$	−16.1823	+	1.81587i	−0.663409	+	0.0744436i
$596$	−12.1183	−	8.80443i	−0.496383	−	0.360643i
$597$	−39.7798	−	0.661121i	−1.62808	−	0.0270579i
$598$	−4.97797	−	1.05810i	−0.203564	−	0.0432689i
$599$	24.6676	−	2.59267i	1.00789	−	0.105933i	0.413830	−	0.910354i	$-0.364191\pi$
$599$	24.6676	−	2.59267i	1.00789	−	0.105933i	0.594060	+	0.804421i	$0.297524\pi$
$600$	3.59191	+	2.70200i	0.146639	+	0.110309i
$601$	3.63278	−	1.18036i	0.148184	−	0.0481479i	−0.233986	−	0.972240i	$-0.575177\pi$
$601$	3.63278	−	1.18036i	0.148184	−	0.0481479i	0.382170	+	0.924092i	$0.375177\pi$
$602$	−21.1484	+	7.03620i	−0.861945	+	0.286774i
$603$	7.93670	+	14.8668i	0.323207	+	0.605423i
$604$	4.51192	−	2.60496i	0.183587	−	0.105994i
$605$	−1.64491	−	30.2703i	−0.0668749	−	1.23066i
$606$	17.8488	−	19.1726i	0.725058	−	0.778833i
$607$	10.2443	+	1.07672i	0.415802	+	0.0437026i	0.310120	−	0.950697i	$-0.399631\pi$
$607$	10.2443	+	1.07672i	0.415802	+	0.0437026i	0.105682	+	0.994400i	$0.466297\pi$
$608$	6.32723	+	2.05584i	0.256603	+	0.0833754i
$609$	−6.39324	+	19.0526i	−0.259067	+	0.772051i
$610$	6.55542	−	4.76279i	0.265421	−	0.192840i
$611$	−8.70364	−	3.87511i	−0.352111	−	0.156770i
$612$	−5.28643	−	4.11601i	−0.213691	−	0.166380i
$613$	−19.8888	+	17.9080i	−0.803302	+	0.723297i	−0.964631	−	0.263604i	$-0.915089\pi$
$613$	−19.8888	+	17.9080i	−0.803302	+	0.723297i	0.161329	+	0.986901i	$0.448422\pi$
$614$	13.7144	+	1.44144i	0.553467	+	0.0581717i
$615$	4.58081	−	19.9176i	0.184716	−	0.803153i
$616$	2.99514	+	8.24798i	0.120678	+	0.332320i
$617$			0.534245i			0.0215079i	0.999942	+	0.0107539i	$0.00342315\pi$
$617$			0.534245i			0.0215079i	−0.999942	+	0.0107539i	$0.996577\pi$
$618$	−0.781034	+	2.27446i	−0.0314178	+	0.0914921i
$619$	6.98455	+	7.75712i	0.280733	+	0.311785i	0.866976	−	0.498350i	$-0.166060\pi$
$619$	6.98455	+	7.75712i	0.280733	+	0.311785i	−0.586243	+	0.810135i	$0.699394\pi$
$620$	0.136506	−	0.642211i	0.00548222	−	0.0257918i
$621$	−25.9127	+	13.2851i	−1.03984	+	0.533111i
$622$	−17.9875	−	24.7577i	−0.721234	−	0.992693i
$623$	−5.33680	+	7.45508i	−0.213815	+	0.298681i
$624$	−1.34892	−	0.808980i	−0.0540000	−	0.0323851i
$625$	3.26557	−	31.0698i	0.130623	−	1.24279i
$626$	5.18410	−	8.97912i	0.207198	−	0.358878i
$627$	22.1371	−	31.1535i	0.884071	−	1.24415i
$628$	−0.595632	−	1.03166i	−0.0237683	−	0.0411679i
$629$	−19.5934	−	14.2354i	−0.781239	−	0.567603i
$630$	−13.3168	+	17.3537i	−0.530553	+	0.691388i
$631$	−9.40698	−	28.9517i	−0.374486	−	1.15255i	−0.943825	−	0.330446i	$-0.892801\pi$
$631$	−9.40698	−	28.9517i	−0.374486	−	1.15255i	0.569339	−	0.822103i	$-0.307199\pi$
$632$	1.94602	−	4.37082i	0.0774083	−	0.173862i
$633$	−42.9648	−	5.23899i	−1.70770	−	0.208231i
$634$	4.86922	−	22.9079i	0.193382	−	0.909789i
$635$	−15.6712	+	3.33101i	−0.621891	+	0.132187i
$636$	−3.71945	+	3.23873i	−0.147486	+	0.128424i
$637$	−1.40891	−	6.19873i	−0.0558229	−	0.245603i
$638$	−13.1220	+	6.27438i	−0.519503	+	0.248405i
$639$	13.1224	−	0.939639i	0.519114	−	0.0371715i
$640$	−1.12093	−	2.51765i	−0.0443086	−	0.0995188i
$641$	2.88041	−	2.59353i	0.113769	−	0.102438i	−0.610283	−	0.792184i	$-0.708944\pi$
$641$	2.88041	−	2.59353i	0.113769	−	0.102438i	0.724052	+	0.689745i	$0.242277\pi$
$642$	−5.74547	+	4.03018i	−0.226756	+	0.159059i
$643$	36.1152	−	26.2392i	1.42425	−	1.03477i	0.433193	−	0.901301i	$-0.357387\pi$
$643$	36.1152	−	26.2392i	1.42425	−	1.03477i	0.991052	−	0.133473i	$-0.0426131\pi$
$644$	10.9487	−	9.99840i	0.431437	−	0.393992i
$645$	−3.53813	−	40.0556i	−0.139314	−	1.57719i
$646$	−3.08908	−	14.5330i	−0.121538	−	0.571793i
$647$	8.39624	+	18.8583i	0.330090	+	0.741395i	0.999999	−	0.00104834i	$-0.000333697\pi$
$647$	8.39624	+	18.8583i	0.330090	+	0.741395i	−0.669909	+	0.742443i	$0.733667\pi$
$648$	−8.90818	+	1.28233i	−0.349946	+	0.0503747i
$649$	−0.568517	−	20.9397i	−0.0223162	−	0.821954i
$650$		−	2.35660i		−	0.0924333i
$651$	1.06565	+	0.237217i	0.0417663	+	0.00929726i
$652$	3.54428	−	10.9082i	0.138805	−	0.427197i
$653$	1.51251	+	1.36187i	0.0591891	+	0.0532941i	0.698194	−	0.715908i	$-0.253987\pi$
$653$	1.51251	+	1.36187i	0.0591891	+	0.0532941i	−0.639005	+	0.769202i	$0.720654\pi$
$654$	0.690861	+	0.0842413i	0.0270148	+	0.00329410i
$655$	43.9736	−	4.62181i	1.71819	−	0.180589i
$656$	−2.86493	+	3.18183i	−0.111857	+	0.124229i
$657$	−23.0429	−	22.1780i	−0.898989	−	0.865246i
$658$	23.9404	−	14.0472i	0.933295	−	0.547617i
$659$	−42.4842			−1.65495			−0.827475	−	0.561503i	$-0.810223\pi$
$659$	−42.4842			−1.65495			−0.827475	+	0.561503i	$0.810223\pi$
$660$	−15.7265	+	1.82047i	−0.612152	+	0.0708617i
$661$	3.30366	−	5.72211i	0.128498	−	0.222564i	−0.794597	−	0.607137i	$-0.792318\pi$
$661$	3.30366	−	5.72211i	0.128498	−	0.222564i	0.923095	+	0.384573i	$0.125651\pi$
$662$	−9.95899	+	4.43403i	−0.387067	+	0.172333i
$663$	−0.0583720	+	3.51226i	−0.00226698	+	0.136405i
$664$	−1.17412	−	3.61356i	−0.0455645	−	0.140233i
$665$	−47.3768	+	10.4187i	−1.83719	+	0.404020i
$666$	−32.0297	+	5.70289i	−1.24112	+	0.220982i
$667$	18.2639	+	16.4449i	0.707180	+	0.636748i
$668$	11.0959	+	12.3232i	0.429312	+	0.476800i
$669$	34.6329	−	6.76199i	1.33899	−	0.261433i
$670$	13.4074	−	7.74074i	0.517971	−	0.299051i
$671$	−1.76784	+	9.58998i	−0.0682467	+	0.370217i
$672$	4.20408	−	1.82366i	0.162176	−	0.0703493i
$673$	−7.43753	+	10.2369i	−0.286696	+	0.394603i	−0.927937	−	0.372736i	$-0.878420\pi$
$673$	−7.43753	+	10.2369i	−0.286696	+	0.394603i	0.641242	+	0.767339i	$0.278420\pi$
$674$	−5.24903	−	24.6948i	−0.202185	−	0.951207i
$675$	−8.51211	−	10.4579i	−0.327631	−	0.402524i
$676$	−1.27267	−	12.1086i	−0.0489488	−	0.465716i
$677$	35.4891	+	15.8007i	1.36396	+	0.607272i	0.952606	−	0.304206i	$-0.0983911\pi$
$677$	35.4891	+	15.8007i	1.36396	+	0.607272i	0.411349	+	0.911478i	$0.365058\pi$
$678$	32.0741	−	2.83312i	1.23180	−	0.108805i
$679$	46.3075	+	9.50339i	1.77712	+	0.364707i
$680$	−3.61765	+	4.97927i	−0.138731	+	0.190946i
$681$	−1.87728	−	6.12201i	−0.0719375	−	0.234596i
$682$	0.413497	+	0.673308i	0.0158336	+	0.0257823i
$683$	16.8137	+	9.70740i	0.643359	+	0.371443i	0.785907	−	0.618345i	$-0.212196\pi$
$683$	16.8137	+	9.70740i	0.643359	+	0.371443i	−0.142549	+	0.989788i	$0.545530\pi$
$684$	−16.9434	−	10.5481i	−0.647849	−	0.403318i
$685$	7.74617	−	23.8403i	0.295966	−	0.910889i
$686$	17.0741	+	7.17457i	0.651893	+	0.273927i
$687$	−21.0245	+	8.94509i	−0.802133	+	0.341276i
$688$	−3.42641	+	7.69584i	−0.130631	+	0.293401i
$689$	2.52930	+	0.537619i	0.0963587	+	0.0204817i
$690$	12.9884	+	23.3856i	0.494460	+	0.890275i
$691$	−0.0343623	+	0.326935i	−0.00130720	+	0.0124372i	−0.995156	−	0.0983078i	$-0.968657\pi$
$691$	−0.0343623	+	0.326935i	−0.00130720	+	0.0124372i	0.993849	+	0.110745i	$0.0353237\pi$
$692$	−11.3971			−0.433253
$693$	−2.77616	−	26.1781i	−0.105457	−	0.994424i
$694$	8.95878			0.340071
$695$	−4.76444	+	45.3306i	−0.180725	+	1.71949i
$696$	3.68807	+	6.64038i	0.139796	+	0.251703i
$697$	9.35299	+	1.98804i	0.354270	+	0.0753024i
$698$	1.63624	−	3.67506i	0.0619327	−	0.139103i
$699$	−20.1366	+	8.56734i	−0.761636	+	0.324047i
$700$	5.58278	+	3.99649i	0.211009	+	0.151053i
$701$	9.58667	−	29.5047i	0.362084	−	1.11438i	−0.589704	−	0.807620i	$-0.700755\pi$
$701$	9.58667	−	29.5047i	0.362084	−	1.11438i	0.951787	−	0.306759i	$-0.0992446\pi$
$702$	3.34499	+	3.32827i	0.126249	+	0.125617i
$703$	−62.4808	−	36.0733i	−2.35651	−	1.36053i
$704$	3.06538	+	1.26626i	0.115531	+	0.0477241i
$705$	14.6816	+	47.8783i	0.552942	+	1.80320i
$706$	14.0680	−	19.3629i	0.529454	−	0.728732i
$707$	26.5645	−	29.9230i	0.999060	−	1.12537i
$708$	−10.8970	+	0.962535i	−0.409534	+	0.0361743i
$709$	−38.1680	−	16.9935i	−1.43343	−	0.638204i	−0.464508	−	0.885569i	$-0.653769\pi$
$709$	−38.1680	−	16.9935i	−1.43343	−	0.638204i	−0.968923	+	0.247364i	$0.920436\pi$
$710$	−1.26329	−	12.0194i	−0.0474103	−	0.451078i
$711$	−8.81792	+	11.3254i	−0.330698	+	0.424734i
$712$	0.720483	+	3.38961i	0.0270012	+	0.127031i
$713$	0.784752	−	1.08012i	0.0293892	−	0.0404508i
$714$	−8.22154	−	6.09463i	−0.307684	−	0.228086i
$715$	5.71948	+	6.01545i	0.213896	+	0.224965i
$716$	−8.56240	+	4.94350i	−0.319992	+	0.184747i
$717$	−7.50596	+	1.46552i	−0.280315	+	0.0547308i
$718$	−17.7065	−	19.6650i	−0.660800	−	0.733893i
$719$	−7.76133	−	6.98833i	−0.289449	−	0.260621i	0.511595	−	0.859227i	$-0.329055\pi$
$719$	−7.76133	−	6.98833i	−0.289449	−	0.260621i	−0.801044	+	0.598606i	$0.795722\pi$
$720$	1.44928	+	8.13971i	0.0540113	+	0.303349i
$721$	−1.11057	+	3.50152i	−0.0413600	+	0.130404i
$722$	−7.80588	−	24.0240i	−0.290505	−	0.894082i
$723$	−0.320947	+	19.3114i	−0.0119361	+	0.718200i
$724$	−14.1103	+	6.28233i	−0.524407	+	0.233481i
$725$	−5.69019	+	9.85570i	−0.211328	+	0.366032i
$726$	12.2064	−	14.6289i	0.453021	−	0.542929i
$727$	40.2565			1.49303			0.746515	−	0.665368i	$-0.231725\pi$
$727$	40.2565			1.49303			0.746515	+	0.665368i	$0.231725\pi$
$728$	−2.08915	−	1.18668i	−0.0774290	−	0.0439812i
$729$	26.8659	+	2.68765i	0.995033	+	0.0995427i
$730$	−19.6589	+	21.8334i	−0.727607	+	0.808089i
$731$	18.7104	−	1.96654i	0.692030	−	0.0727352i
$732$	5.05514	+	0.616408i	0.186844	+	0.0227831i
$733$	−4.49741	−	4.04948i	−0.166115	−	0.149571i	0.581881	−	0.813274i	$-0.302317\pi$
$733$	−4.49741	−	4.04948i	−0.166115	−	0.149571i	−0.747996	+	0.663703i	$0.768984\pi$
$734$	2.89291	−	8.90345i	0.106779	−	0.328633i
$735$	−19.7093	+	26.9817i	−0.726989	+	0.995236i
$736$		−	5.60409i		−	0.206570i
$737$	−5.27437	+	17.8692i	−0.194284	+	0.658220i
$738$	10.6367	−	7.20045i	0.391544	−	0.265052i
$739$	7.30925	+	16.4169i	0.268875	+	0.603904i	0.996639	−	0.0819247i	$-0.0261067\pi$
$739$	7.30925	+	16.4169i	0.268875	+	0.603904i	−0.727763	+	0.685828i	$0.759440\pi$
$740$	6.21373	+	29.2333i	0.228421	+	1.07464i
$741$	0.920732	+	10.4237i	0.0338239	+	0.382925i
$742$	−5.56300	+	5.08018i	−0.204224	+	0.186499i
$743$	27.5255	−	19.9984i	1.00981	−	0.733672i	0.0456429	−	0.998958i	$-0.485466\pi$
$743$	27.5255	−	19.9984i	1.00981	−	0.733672i	0.964170	+	0.265286i	$0.0854664\pi$
$744$	0.337815	−	0.236962i	0.0123849	−	0.00868743i
$745$	30.6776	−	27.6222i	1.12394	−	1.01200i
$746$	−9.97970	−	22.4148i	−0.365383	−	0.820663i
$747$	0.814118	+	11.3694i	0.0297870	+	0.415986i
$748$	−0.973877	−	7.34265i	−0.0356085	−	0.268474i
$749$	−8.62835	+	6.36197i	−0.315273	+	0.232461i
$750$	8.65763	−	7.53867i	0.316132	−	0.275273i
$751$	1.92014	−	0.408137i	0.0700667	−	0.0148931i	−0.172745	−	0.984967i	$-0.555264\pi$
$751$	1.92014	−	0.408137i	0.0700667	−	0.0148931i	0.242812	+	0.970073i	$0.421930\pi$
$752$	2.18126	−	10.2620i	0.0795423	−	0.374217i
$753$	−41.5340	−	5.06453i	−1.51358	−	0.184562i
$754$	1.61983	−	3.63820i	0.0589908	−	0.132495i
$755$	4.43688	+	13.6553i	0.161475	+	0.496968i
$756$	−13.5574	+	2.27995i	−0.493076	+	0.0829212i
$757$	14.6142	+	10.6179i	0.531163	+	0.385913i	0.820793	−	0.571226i	$-0.193532\pi$
$757$	14.6142	+	10.6179i	0.531163	+	0.385913i	−0.289629	+	0.957139i	$0.593532\pi$
$758$	−11.9262	−	20.6567i	−0.433178	−	0.750286i
$759$	−30.7204	−	9.62539i	−1.11508	−	0.349380i
$760$	−9.16732	+	15.8783i	−0.332534	+	0.575965i
$761$	−0.925539	+	8.80591i	−0.0335507	+	0.319214i	0.964856	+	0.262781i	$0.0846395\pi$
$761$	−0.925539	+	8.80591i	−0.0335507	+	0.319214i	−0.998406	+	0.0564334i	$0.982027\pi$
$762$	−8.63527	−	5.17878i	−0.312823	−	0.187608i
$763$	1.05805	+	0.103695i	0.0383041	+	0.00375401i
$764$	−12.0665	−	16.6081i	−0.436550	−	0.600860i
$765$	14.1245	−	11.8921i	0.510673	−	0.429961i
$766$	−4.04752	+	19.0421i	−0.146243	+	0.688018i
$767$	3.83784	+	4.26235i	0.138576	+	0.153905i
$768$	0.562532	−	1.63816i	0.0202986	−	0.0591119i
$769$		−	5.92488i		−	0.213657i	−0.994277	−	0.106828i	$-0.965930\pi$
$769$		−	5.92488i		−	0.213657i	0.994277	−	0.106828i	$-0.0340695\pi$
$770$	−23.9501	+	3.34798i	−0.863103	+	0.120653i
$771$	−2.08842	+	9.08053i	−0.0752125	+	0.327027i
$772$	23.7227	+	2.49336i	0.853799	+	0.0897379i
$773$	−24.0733	+	21.6757i	−0.865855	+	0.779619i	−0.976788	−	0.214209i	$-0.931283\pi$
$773$	−24.0733	+	21.6757i	−0.865855	+	0.779619i	0.110933	+	0.993828i	$0.464616\pi$
$774$	15.5260	−	19.9409i	0.558070	−	0.716761i
$775$	0.564783	+	0.251458i	0.0202876	+	0.00903262i
$776$	14.4550	−	10.5022i	0.518905	−	0.377006i
$777$	−48.7065	+	9.86559i	−1.74734	+	0.353926i
$778$	14.2585	+	4.63286i	0.511191	+	0.166096i
$779$	28.3286	+	2.97745i	1.01498	+	0.106678i
$780$	2.95367	−	3.17273i	0.105758	−	0.113602i
$781$	11.0688	+	9.43523i	0.396073	+	0.337619i
$782$	−10.8387	+	6.25775i	−0.387593	+	0.223777i
$783$	−5.95297	−	21.9961i	−0.212742	−	0.786078i
$784$	6.35418	−	2.93674i	0.226935	−	0.104884i
$785$	3.12233	−	1.01451i	0.111441	−	0.0362093i
$786$	22.2073	+	16.7053i	0.792106	+	0.595858i
$787$	5.51325	−	0.579466i	0.196526	−	0.0206557i	−0.00575389	−	0.999983i	$-0.501832\pi$
$787$	5.51325	−	0.579466i	0.196526	−	0.0206557i	0.202280	+	0.979328i	$0.435165\pi$
$788$	16.3934	+	3.48452i	0.583990	+	0.124131i
$789$	23.8277	+	0.396004i	0.848288	+	0.0140981i
$790$	10.6673	+	7.75026i	0.379526	+	0.275742i
$791$	48.8779	−	5.48477i	1.73790	−	0.195016i
$792$	−8.01384	−	5.89732i	−0.284759	−	0.209552i
$793$	−1.33503	−	2.31234i	−0.0474082	−	0.0821134i
$794$	−22.5069	+	10.0207i	−0.798739	+	0.355621i
$795$	−6.59939	−	11.8822i	−0.234056	−	0.421418i
$796$	−15.3700	+	17.0701i	−0.544774	+	0.605033i
$797$	12.1374	+	16.7057i	0.429929	+	0.591747i	0.967937	−	0.251193i	$-0.0808229\pi$
$797$	12.1374	+	16.7057i	0.429929	+	0.591747i	−0.538008	+	0.842940i	$0.680823\pi$
$798$	−26.2552	−	15.4961i	−0.929426	−	0.548557i
$799$	−22.2832	+	7.24025i	−0.788323	+	0.256142i
$800$	2.53833	−	0.539538i	0.0897434	−	0.0190755i
$801$	0.345457	−	10.3903i	0.0122061	−	0.367122i
$802$	21.0288	+	12.1410i	0.742552	+	0.428712i
$803$	−0.959605	−	35.3442i	−0.0338637	−	1.24727i
$804$	9.48235	+	2.18083i	0.334417	+	0.0769120i
$805$	20.6791	+	35.2431i	0.728843	+	1.24215i
$806$	−0.205758	−	0.0668549i	−0.00724752	−	0.00235486i
$807$	−6.29408	−	8.97291i	−0.221562	−	0.315861i
$808$	−1.58084	−	15.0407i	−0.0556139	−	0.529131i
$809$	−3.70144	−	35.2168i	−0.130136	−	1.23816i	−0.843409	−	0.537272i	$-0.819455\pi$
$809$	−3.70144	−	35.2168i	−0.130136	−	1.23816i	0.713273	−	0.700886i	$-0.247212\pi$
$810$	1.64750	−	24.7484i	0.0578873	−	0.869570i
$811$	9.00660	+	2.92642i	0.316265	+	0.102761i	0.462848	−	0.886438i	$-0.346828\pi$
$811$	9.00660	+	2.92642i	0.316265	+	0.102761i	−0.146583	+	0.989198i	$0.546828\pi$
$812$	5.87186	+	10.0073i	0.206062	+	0.351188i
$813$	0.887282	−	3.85794i	0.0311183	−	0.135304i
$814$	−29.6610	−	20.3434i	−1.03962	−	0.713035i
$815$	27.3742	+	15.8045i	0.958875	+	0.553607i
$816$	−3.79647	+	0.741250i	−0.132903	+	0.0259489i
$817$	54.8198	−	11.6523i	1.91790	−	0.407663i
$818$	−25.5696	+	8.30805i	−0.894019	+	0.290484i
$819$	5.22833	+	4.96179i	0.182693	+	0.173379i
$820$	−6.93564	−	9.54609i	−0.242203	−	0.333364i
$821$	14.3879	−	15.9794i	0.502141	−	0.557684i	−0.437777	−	0.899083i	$-0.644234\pi$
$821$	14.3879	−	15.9794i	0.502141	−	0.557684i	0.939918	+	0.341399i	$0.110901\pi$
$822$	13.7727	−	7.64937i	0.480377	−	0.266802i
$823$	−5.99816	+	2.67055i	−0.209083	+	0.0930896i	−0.508606	−	0.860999i	$-0.669839\pi$
$823$	−5.99816	+	2.67055i	−0.209083	+	0.0930896i	0.299523	+	0.954089i	$0.403172\pi$
$824$	0.694212	+	1.20241i	0.0241840	+	0.0418880i
$825$	1.40211	−	14.8412i	0.0488151	−	0.516706i
$826$	−16.6060	+	1.86342i	−0.577797	+	0.0648367i
$827$	39.8068	+	28.9213i	1.38422	+	1.00569i	0.996472	+	0.0839259i	$0.0267459\pi$
$827$	39.8068	+	28.9213i	1.38422	+	1.00569i	0.387745	+	0.921767i	$0.373254\pi$
$828$	−4.04000	+	16.3197i	−0.140400	+	0.567147i
$829$	−0.584827	−	0.124309i	−0.0203119	−	0.00431743i	0.197745	−	0.980254i	$-0.436638\pi$
$829$	−0.584827	−	0.124309i	−0.0203119	−	0.00431743i	−0.218056	+	0.975936i	$0.569972\pi$
$830$	10.4138	−	1.09453i	0.361467	−	0.0379917i
$831$	−9.56553	+	12.7160i	−0.331824	+	0.441112i
$832$	−0.863672	+	0.280624i	−0.0299424	+	0.00972889i
$833$	−12.7752	−	9.01019i	−0.442635	−	0.312185i
$834$	−21.6042	+	18.8119i	−0.748091	+	0.651403i
$835$	−39.5773	+	22.8500i	−1.36963	+	0.790756i
$836$	−5.17164	−	21.4504i	−0.178865	−	0.741876i
$837$	−1.15458	+	0.446523i	−0.0399080	+	0.0154341i
$838$	9.06724	+	0.953006i	0.313223	+	0.0329210i
$839$	35.2570	+	11.4557i	1.21721	+	0.395494i	0.846063	−	0.533082i	$-0.178966\pi$
$839$	35.2570	+	11.4557i	1.21721	+	0.395494i	0.371142	+	0.928576i	$0.378966\pi$
$840$	2.50715	+	12.3778i	0.0865048	+	0.427075i
$841$	7.90235	−	5.74139i	0.272495	−	0.197979i
$842$	−15.6834	−	6.98270i	−0.540485	−	0.240640i
$843$	10.1904	+	4.74153i	0.350978	+	0.163307i
$844$	−18.5708	+	16.7212i	−0.639233	+	0.575568i
$845$	33.3703	+	3.50736i	1.14797	+	0.120657i
$846$	−13.7499	+	28.3115i	−0.472732	+	0.973369i
$847$	18.1120	−	22.7806i	0.622337	−	0.782750i
$848$			2.84743i			0.0977813i
$849$	10.8068	+	3.71098i	0.370888	+	0.127360i
$850$	−3.87790	−	4.30685i	−0.133011	−	0.147724i
$851$	−12.6355	+	59.4454i	−0.433140	+	2.03776i
$852$	4.56608	−	6.06994i	0.156431	−	0.207953i
$853$	−3.16081	−	4.35048i	−0.108224	−	0.148958i	0.751469	−	0.659768i	$-0.229345\pi$
$853$	−3.16081	−	4.35048i	−0.108224	−	0.148958i	−0.859693	+	0.510810i	$0.829345\pi$
$854$	7.74196	+	0.758753i	0.264925	+	0.0259640i
$855$	38.1428	−	39.6303i	1.30446	−	1.35533i
$856$	−0.423535	+	4.02967i	−0.0144761	+	0.137731i
$857$	−10.1726	+	17.6194i	−0.347488	+	0.601867i	−0.985803	−	0.167909i	$-0.946299\pi$
$857$	−10.1726	+	17.6194i	−0.347488	+	0.601867i	0.638315	+	0.769776i	$0.279632\pi$
$858$	0.0549083	+	5.21645i	0.00187454	+	0.178087i
$859$	−17.2318	−	29.8464i	−0.587941	−	1.01834i	−0.994502	−	0.104721i	$-0.966605\pi$
$859$	−17.2318	−	29.8464i	−0.587941	−	1.01834i	0.406560	−	0.913624i	$-0.366728\pi$
$860$	−18.7823	−	13.6461i	−0.640470	−	0.465329i
$861$	15.9833	−	11.3799i	0.544709	−	0.387827i
$862$	12.1149	+	37.2859i	0.412636	+	1.26996i
$863$	−18.0794	+	40.6070i	−0.615430	+	1.38228i	0.289689	+	0.957121i	$0.406448\pi$
$863$	−18.0794	+	40.6070i	−0.615430	+	1.38228i	−0.905119	+	0.425158i	$0.860219\pi$
$864$	−2.81910	+	4.36494i	−0.0959077	+	0.148498i
$865$	6.53039	−	30.7230i	0.222040	−	1.04461i
$866$	7.28215	−	1.54787i	0.247458	−	0.0525987i
$867$	−13.6632	−	15.6912i	−0.464027	−	0.532902i
$868$	0.507320	−	0.374064i	0.0172195	−	0.0126965i
$869$	−15.7305	+	2.08638i	−0.533621	+	0.0707757i
$870$	−20.0136	+	6.13705i	−0.678524	+	0.208065i
$871$	−2.07493	−	4.66037i	−0.0703063	−	0.157911i
$872$	0.298613	−	0.268872i	0.0101123	−	0.00910516i
$873$	−49.6654	+	20.1627i	−1.68092	+	0.682404i
$874$	−30.1627	+	21.9145i	−1.02027	+	0.741269i
$875$	12.9488	−	11.8249i	0.437749	−	0.399756i
$876$	−18.3931	+	1.62467i	−0.621446	+	0.0548926i
$877$	3.80533	+	17.9027i	0.128497	+	0.604530i	0.994522	+	0.104529i	$0.0333336\pi$
$877$	3.80533	+	17.9027i	0.128497	+	0.604530i	−0.866025	+	0.500001i	$0.833333\pi$
$878$	11.3561	+	25.5061i	0.383248	+	0.860790i
$879$	15.1172	−	16.2384i	0.509891	−	0.547708i
$880$	−5.16987	+	7.53776i	−0.174276	+	0.254098i
$881$			10.9054i			0.367412i	0.982981	+	0.183706i	$0.0588094\pi$
$881$			10.9054i			0.367412i	−0.982981	+	0.183706i	$0.941191\pi$
$882$	−20.6211	+	3.97133i	−0.694348	+	0.133722i
$883$	−1.16254	+	3.57794i	−0.0391227	+	0.120407i	−0.968710	−	0.248194i	$-0.920163\pi$
$883$	−1.16254	+	3.57794i	−0.0391227	+	0.120407i	0.929588	+	0.368601i	$0.120163\pi$
$884$	1.50716	+	1.35705i	0.0506912	+	0.0456426i
$885$	3.64912	−	29.9264i	0.122664	−	1.00596i
$886$	−5.79421	+	0.608996i	−0.194660	+	0.0204596i
$887$	30.2166	−	33.5589i	1.01457	−	1.12680i	0.0226791	−	0.999743i	$-0.492780\pi$
$887$	30.2166	−	33.5589i	1.01457	−	1.12680i	0.991895	−	0.127056i	$-0.0405529\pi$
$888$	−9.66060	+	16.1084i	−0.324188	+	0.540563i
$889$	−13.3739	−	7.59665i	−0.448547	−	0.254784i
$890$	−9.55014			−0.320121
$891$	19.0857	+	22.9508i	0.639394	+	0.768879i
$892$	10.1864	−	17.6434i	0.341067	−	0.590746i
$893$	−63.7626	+	28.3889i	−2.13373	+	0.949999i
$894$	25.9408	+	0.431123i	0.867590	+	0.0144189i
$895$	−8.42000	−	25.9141i	−0.281450	−	0.866213i
$896$	0.799882	−	2.52194i	0.0267222	−	0.0842522i
$897$	8.11111	−	3.45096i	0.270822	−	0.115224i
$898$	−8.75167	−	7.88004i	−0.292047	−	0.262960i
$899$	0.699090	+	0.776419i	0.0233160	+	0.0258950i
$900$	−7.78080	−	0.258698i	−0.259360	−	0.00862325i
$901$	5.50716	−	3.17956i	0.183470	−	0.105926i
$902$	13.9651	+	2.57435i	0.464986	+	0.0857166i
$903$	22.9895	−	31.0124i	0.765044	−	1.03203i
$904$	10.9270	−	15.0397i	0.363425	−	0.500212i
$905$	−8.85016	−	41.6367i	−0.294189	−	1.38405i
$906$	−3.80681	+	8.18156i	−0.126473	+	0.271814i
$907$	5.58670	+	53.1539i	0.185503	+	1.76495i	0.551352	+	0.834273i	$0.314112\pi$
$907$	5.58670	+	53.1539i	0.185503	+	1.76495i	−0.365848	+	0.930675i	$0.619221\pi$
$908$	−3.37737	−	1.50370i	−0.112082	−	0.0499021i
$909$	−6.23932	+	44.9397i	−0.206945	+	1.49055i
$910$	4.39596	−	4.95174i	0.145725	−	0.164149i
$911$	−18.7287	+	25.7778i	−0.620509	+	0.854057i	−0.997390	−	0.0722044i	$-0.976997\pi$
$911$	−18.7287	+	25.7778i	−0.620509	+	0.854057i	0.376881	+	0.926262i	$0.376997\pi$
$912$	−11.0167	+	3.37822i	−0.364801	+	0.111864i
$913$	−8.17483	+	9.59019i	−0.270547	+	0.317389i
$914$	−26.1310	−	15.0868i	−0.864338	−	0.499026i
$915$	−4.55817	+	13.2739i	−0.150688	+	0.438821i
$916$	−4.07638	+	12.5458i	−0.134687	+	0.414525i
$917$	34.5160	+	24.7086i	1.13982	+	0.815951i
$918$	11.5900	+	0.578289i	0.382529	+	0.0190864i
$919$	9.71005	−	21.8091i	0.320305	−	0.719417i	−0.679595	−	0.733588i	$-0.737844\pi$
$919$	9.71005	−	21.8091i	0.320305	−	0.719417i	0.999900	+	0.0141710i	$0.00451093\pi$
$920$	15.1069	+	3.21106i	0.498059	+	0.105866i
$921$	−20.8805	+	11.5970i	−0.688035	+	0.382136i
$922$	1.15702	−	11.0083i	0.0381045	−	0.362540i
$923$	−3.98240			−0.131082
$924$	−12.4509	−	8.71638i	−0.409604	−	0.286748i
$925$	−28.1418			−0.925296
$926$	−0.306448	+	2.91566i	−0.0100705	+	0.0958145i
$927$	−1.15479	−	4.00199i	−0.0379284	−	0.131443i
$928$	4.28962	+	0.911786i	0.140814	+	0.0299308i
$929$	18.7080	−	42.0189i	0.613790	−	1.37859i	−0.292634	−	0.956225i	$-0.594532\pi$
$929$	18.7080	−	42.0189i	0.613790	−	1.37859i	0.906424	−	0.422370i	$-0.138802\pi$
$930$	0.445211	+	1.04642i	0.0145990	+	0.0343134i
$931$	−40.6540	−	22.7159i	−1.33238	−	0.744484i
$932$	−3.90424	+	12.0160i	−0.127887	+	0.393597i
$933$	50.1312	+	17.2147i	1.64122	+	0.563585i
$934$	30.9918	+	17.8931i	1.01408	+	0.585481i
$935$	20.3515	+	1.58197i	0.665565	+	0.0517358i
$936$	2.71740	−	0.194581i	0.0888209	−	0.00636009i
$937$	−1.10579	+	1.52199i	−0.0361246	+	0.0497213i	−0.826697	−	0.562647i	$-0.809783\pi$
$937$	−1.10579	+	1.52199i	−0.0361246	+	0.0497213i	0.790573	+	0.612368i	$0.209783\pi$
$938$	14.5592	+	2.98790i	0.475376	+	0.0975583i
$939$	1.58011	+	17.8886i	0.0515648	+	0.583772i
$940$	26.4133	+	11.7600i	0.861508	+	0.383568i
$941$	−3.01561	−	28.6916i	−0.0983062	−	0.935321i	−0.926859	−	0.375410i	$-0.877502\pi$
$941$	−3.01561	−	28.6916i	−0.0983062	−	0.935321i	0.828553	−	0.559911i	$-0.189165\pi$
$942$	1.87074	+	0.870438i	0.0609520	+	0.0283604i
$943$	−4.98870	−	23.4700i	−0.162454	−	0.764288i
$944$	−3.71238	+	5.10965i	−0.120828	+	0.166305i
$945$	1.62213	−	37.8527i	0.0527678	−	1.23135i
$946$	27.6972	−	3.67356i	0.900513	−	0.119438i
$947$	−14.5984	+	8.42840i	−0.474385	+	0.273886i	−0.718073	−	0.695967i	$-0.754976\pi$
$947$	−14.5984	+	8.42840i	−0.474385	+	0.273886i	0.243689	+	0.969853i	$0.421642\pi$
$948$	1.58802	+	8.13335i	0.0515763	+	0.264159i
$949$	6.47792	+	7.19446i	0.210282	+	0.233542i
$950$	−12.8299	−	11.5521i	−0.416257	−	0.374800i
$951$	15.8808	+	37.3262i	0.514971	+	1.21038i
$952$	−5.77081	+	1.26907i	−0.187033	+	0.0411307i
$953$	−9.78823	−	30.1251i	−0.317072	−	0.975847i	−0.974893	−	0.222673i	$-0.928522\pi$
$953$	−9.78823	−	30.1251i	−0.317072	−	0.975847i	0.657821	−	0.753174i	$-0.271478\pi$
$954$	2.05272	−	8.29200i	0.0664593	−	0.268463i
$955$	51.6842	−	23.0113i	1.67246	−	0.744627i
$956$	−2.20770	+	3.82385i	−0.0714021	+	0.123672i
$957$	12.3659	−	21.9487i	0.399733	−	0.709501i
$958$	−19.3980			−0.626721
$959$	20.7560	−	12.1787i	0.670246	−	0.393271i
$960$	4.09363	+	2.45505i	0.132121	+	0.0792364i
$961$	−20.7051	+	22.9953i	−0.667906	+	0.741784i
$962$	9.79411	−	1.02940i	0.315775	−	0.0331893i
$963$	4.13837	−	11.4294i	0.133357	−	0.368309i
$964$	8.28681	+	7.46148i	0.266900	+	0.240318i
$965$	−20.3141	+	62.5203i	−0.653934	+	2.01260i
$966$	−5.58011	+	25.0676i	−0.179537	+	0.806537i
$967$			0.0899523i			0.00289267i	0.999999	+	0.00144634i	$0.000460383\pi$
$967$			0.0899523i			0.00289267i	−0.999999	+	0.00144634i	$0.999540\pi$
$968$	−1.74171	−	10.8612i	−0.0559808	−	0.349093i
$969$	18.8355	+	17.5350i	0.605083	+	0.563305i
$970$	20.0281	+	44.9838i	0.643062	+	1.44434i
$971$	1.22134	+	5.74596i	0.0391947	+	0.184397i	0.993390	−	0.114788i	$-0.0366188\pi$
$971$	1.22134	+	5.74596i	0.0391947	+	0.184397i	−0.954195	+	0.299184i	$0.903285\pi$
$972$	11.3562	−	10.6788i	0.364249	−	0.342523i
$973$	−32.3123	+	29.5079i	−1.03588	+	0.945978i
$974$	6.52373	−	4.73977i	0.209034	−	0.151872i
$975$	2.34399	+	3.34161i	0.0750676	+	0.107017i
$976$	2.18500	−	1.96738i	0.0699401	−	0.0629744i
$977$	14.8825	+	33.4266i	0.476133	+	1.06941i	0.978779	+	0.204920i	$0.0656934\pi$
$977$	14.8825	+	33.4266i	0.476133	+	1.06941i	−0.502646	+	0.864493i	$0.667640\pi$
$978$	5.82406	+	18.9929i	0.186233	+	0.607326i
$979$	8.32925	−	7.91943i	0.266204	−	0.253106i
$980$	4.27567	+	18.8116i	0.136581	+	0.600914i
$981$	−1.06342	+	0.567711i	−0.0339524	+	0.0181256i
$982$	−26.1987	+	5.56870i	−0.836033	+	0.177704i
$983$	8.19645	−	38.5613i	0.261426	−	1.22991i	−0.629945	−	0.776640i	$-0.716923\pi$
$983$	8.19645	−	38.5613i	0.261426	−	1.22991i	0.891371	−	0.453274i	$-0.149744\pi$
$984$	0.897622	−	7.36137i	0.0286151	−	0.234672i
$985$	−18.7864	+	42.1949i	−0.598583	+	1.34444i
$986$	−3.02649	−	9.31459i	−0.0963832	−	0.296637i
$987$	−19.9751	+	43.7310i	−0.635813	+	1.39197i
$988$	4.88773	+	3.55115i	0.155500	+	0.112977i
$989$	−23.6048	−	40.8848i	−0.750590	−	1.30006i
$990$	20.4891	−	18.2237i	0.651188	−	0.579187i
$991$	0.245349	−	0.424956i	0.00779376	−	0.0134992i	−0.862102	−	0.506734i	$-0.830852\pi$
$991$	0.245349	−	0.424956i	0.00779376	−	0.0134992i	0.869896	+	0.493235i	$0.164186\pi$
$992$	0.0249025	−	0.236932i	0.000790655	−	0.00752258i
$993$	9.71138	−	16.1931i	0.308181	−	0.513871i
$994$	6.75365	−	9.43430i	0.214213	−	0.299238i
$995$	−37.2088	−	51.2135i	−1.17960	−	1.62358i
$996$	5.25909	+	3.95613i	0.166641	+	0.125355i
$997$	4.98138	−	23.4356i	0.157762	−	0.742212i	−0.826135	−	0.563473i	$-0.809465\pi$
$997$	4.98138	−	23.4356i	0.157762	−	0.742212i	0.983897	−	0.178739i	$-0.0572018\pi$
$998$	−6.22535	−	6.91395i	−0.197060	−	0.218857i
$999$	39.7452	−	39.9449i	1.25748	−	1.26380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.95.6	yes	128
3.2	odd	2		462.2.bc.a.95.4	✓	128
7.2	even	3	inner	462.2.bc.b.359.16	yes	128
11.8	odd	10		462.2.bc.a.305.15	yes	128
21.2	odd	6		462.2.bc.a.359.15	yes	128
33.8	even	10	inner	462.2.bc.b.305.16	yes	128
77.30	odd	30		462.2.bc.a.107.4	yes	128
231.107	even	30	inner	462.2.bc.b.107.6	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.4	✓	128	3.2	odd	2
462.2.bc.a.107.4	yes	128	77.30	odd	30
462.2.bc.a.305.15	yes	128	11.8	odd	10
462.2.bc.a.359.15	yes	128	21.2	odd	6
462.2.bc.b.95.6	yes	128	1.1	even	1	trivial
462.2.bc.b.107.6	yes	128	231.107	even	30	inner
462.2.bc.b.305.16	yes	128	33.8	even	10	inner
462.2.bc.b.359.16	yes	128	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.840980 - 1.51418i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.12093 - 2.51765i) q^{5} +(1.59380 - 0.678098i) q^{6} +(2.40939 - 1.09308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.58551 + 2.54680i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.840980 - 1.51418i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.12093 - 2.51765i) q^{5} +(1.59380 - 0.678098i) q^{6} +(2.40939 - 1.09308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.58551 + 2.54680i) q^{9} +(2.38669 + 1.37795i) q^{10} +(-3.22424 + 0.777358i) q^{11} +(0.507786 + 1.65594i) q^{12} +(0.533779 - 0.734683i) q^{13} +(0.835242 + 2.51045i) q^{14} +(-4.75486 + 0.419999i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.233441 - 2.22105i) q^{17} +(-2.36711 - 1.84303i) q^{18} +(-1.38320 - 6.50747i) q^{19} +(-1.61988 + 2.22958i) q^{20} +(-3.68138 - 2.72901i) q^{21} +(-0.436075 - 3.28783i) q^{22} +(-4.85329 + 2.80205i) q^{23} +(-1.69995 + 0.331911i) q^{24} +(-1.73642 - 1.92849i) q^{25} +(0.674863 + 0.607650i) q^{26} +(5.18970 + 0.258941i) q^{27} +(-2.58401 + 0.568253i) q^{28} +(-1.35518 - 4.17081i) q^{29} +(0.0793202 - 4.77271i) q^{30} +(-0.217640 + 0.0968995i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.88858 + 4.22835i) q^{33} +2.23328 q^{34} +(-0.0512330 - 7.29127i) q^{35} +(2.08037 - 2.16150i) q^{36} +(7.25637 - 8.05901i) q^{37} +(6.61640 - 0.695412i) q^{38} +(-1.56134 - 0.190385i) q^{39} +(-2.04804 - 1.84406i) q^{40} +(-1.32308 + 4.07202i) q^{41} +(3.09886 - 3.37595i) q^{42} +8.42414i q^{43} +(3.31540 - 0.0900140i) q^{44} +(4.63470 + 6.84652i) q^{45} +(-2.27939 - 5.11959i) q^{46} +(-2.18126 - 10.2620i) q^{47} +(-0.152399 - 1.72533i) q^{48} +(4.61035 - 5.26732i) q^{49} +(2.09943 - 1.52532i) q^{50} +(-3.16675 + 2.22133i) q^{51} +(-0.674863 + 0.607650i) q^{52} +(1.15816 + 2.60126i) q^{53} +(-0.799994 + 5.13420i) q^{54} +(-1.65703 + 8.98886i) q^{55} +(-0.295038 - 2.62925i) q^{56} +(-8.69025 + 7.56707i) q^{57} +(4.28962 - 0.911786i) q^{58} +(-1.31314 + 6.17786i) q^{59} +(4.73828 + 0.577770i) q^{60} +(1.19589 - 2.68601i) q^{61} +(-0.0736192 - 0.226576i) q^{62} +(-1.03625 + 7.86932i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.25135 - 2.16739i) q^{65} +(-4.61165 + 3.42530i) q^{66} +(2.80878 - 4.86495i) q^{67} +(-0.233441 + 2.22105i) q^{68} +(8.32433 + 4.99230i) q^{69} +(7.25668 + 0.711193i) q^{70} +(-2.57763 - 3.54780i) q^{71} +(1.93220 + 2.29491i) q^{72} +(-2.21647 + 10.4277i) q^{73} +(7.25637 + 8.05901i) q^{74} +(-1.45979 + 4.25107i) q^{75} +6.65285i q^{76} +(-6.91874 + 5.39731i) q^{77} +(0.352547 - 1.53289i) q^{78} +(4.75825 + 0.500112i) q^{79} +(2.04804 - 1.84406i) q^{80} +(-3.97235 - 8.07592i) q^{81} +(-3.91141 - 1.74147i) q^{82} +(3.07387 - 2.23330i) q^{83} +(3.03354 + 3.43477i) q^{84} +(-5.85348 - 1.90191i) q^{85} +(-8.37800 - 0.880563i) q^{86} +(-5.17569 + 5.55956i) q^{87} +(-0.257033 + 3.30665i) q^{88} +(-3.00107 + 1.73267i) q^{89} +(-7.29347 + 3.89365i) q^{90} +(0.483015 - 2.35360i) q^{91} +(5.32981 - 1.73176i) q^{92} +(0.329755 + 0.248056i) q^{93} +(10.4338 - 1.09664i) q^{94} +(-17.9340 - 3.81199i) q^{95} +(1.73181 + 0.0287819i) q^{96} +(14.4550 + 10.5022i) q^{97} +(4.75655 + 5.13568i) q^{98} +(3.13227 - 9.44399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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